AA Section 11-3 Day 2
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Transcript of AA Section 11-3 Day 2
![Page 1: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/1.jpg)
Section 11-3The fun part
Tuesday, March 3, 2009
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Discriminant Theorem for Factoring Quadratics
Tuesday, March 3, 2009
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Discriminant Theorem for Factoring Quadratics
A polynomial ax2 + bx + c can be factored into first degree (linear) polynomials IFF the discriminant D = b2 - 4ac is a perfect square.
Tuesday, March 3, 2009
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Discriminant Theorem for Factoring Quadratics
A polynomial ax2 + bx + c can be factored into first degree (linear) polynomials IFF the discriminant D = b2 - 4ac is a perfect square.
Is there anything the discriminant CAN’T do?!
Tuesday, March 3, 2009
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Prime/Irreducible
Tuesday, March 3, 2009
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Prime/Irreducible
A polynomial that cannot be factored into lower-degree polynomials with rational coefficients.
Tuesday, March 3, 2009
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Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
Tuesday, March 3, 2009
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Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
Tuesday, March 3, 2009
![Page 9: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/9.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
Tuesday, March 3, 2009
![Page 10: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/10.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
Tuesday, March 3, 2009
![Page 11: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/11.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
Tuesday, March 3, 2009
![Page 12: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/12.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
Tuesday, March 3, 2009
![Page 13: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/13.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
Tuesday, March 3, 2009
![Page 14: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/14.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
b2 - 4ac
Tuesday, March 3, 2009
![Page 15: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/15.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
b2 - 4ac
= 02 - 4(1)(-10)
Tuesday, March 3, 2009
![Page 16: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/16.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
b2 - 4ac
= 02 - 4(1)(-10)
= 40
Tuesday, March 3, 2009
![Page 17: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/17.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
b2 - 4ac
= 02 - 4(1)(-10)
= 40
40 is not a perfect square
Tuesday, March 3, 2009
![Page 18: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/18.jpg)
Example 1Determine whether the following are prime.
a. x2 - 9 b. x2 - 10
b2 - 4ac
= 02 - 4(1)(-9)
= 36
36 is a perfect square
This one is factorable!
It’s also a difference of squares!
b2 - 4ac
= 02 - 4(1)(-10)
= 40
40 is not a perfect square
This one is not factorable!
Tuesday, March 3, 2009
![Page 19: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/19.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
Tuesday, March 3, 2009
![Page 20: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/20.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac
Tuesday, March 3, 2009
![Page 21: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/21.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20)
Tuesday, March 3, 2009
![Page 22: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/22.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49
Tuesday, March 3, 2009
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Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480
Tuesday, March 3, 2009
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Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
Tuesday, March 3, 2009
![Page 25: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/25.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
529 is a perfect square
Tuesday, March 3, 2009
![Page 26: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/26.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
529 is a perfect square (23 ⋅ 23 = 529)
Tuesday, March 3, 2009
![Page 27: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/27.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
529 is a perfect square (23 ⋅ 23 = 529)so this quadratic is factorable.
Tuesday, March 3, 2009
![Page 28: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/28.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
529 is a perfect square (23 ⋅ 23 = 529)so this quadratic is factorable.
. . .
Tuesday, March 3, 2009
![Page 29: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/29.jpg)
Example 2Can 6m2 - 7m - 20 be factored? If so, factor it.
b2 - 4ac = (-7)2 - 4(6)(-20) = 49 + 480 = 529
529 is a perfect square (23 ⋅ 23 = 529)so this quadratic is factorable.
. . .
How do we factor this?
Tuesday, March 3, 2009
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There is a pattern!First, multiply a and c.
Tuesday, March 3, 2009
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There is a pattern!First, multiply a and c.
(6)(-20) =
Tuesday, March 3, 2009
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There is a pattern!First, multiply a and c.
(6)(-20) = -120
Tuesday, March 3, 2009
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There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
Tuesday, March 3, 2009
![Page 34: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/34.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120
Tuesday, March 3, 2009
![Page 35: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/35.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 =
Tuesday, March 3, 2009
![Page 36: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/36.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58
Tuesday, March 3, 2009
![Page 37: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/37.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
Tuesday, March 3, 2009
![Page 38: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/38.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
The two factors need to be much closer.
Tuesday, March 3, 2009
![Page 39: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/39.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
The two factors need to be much closer.
(8)(-15) = -120
Tuesday, March 3, 2009
![Page 40: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/40.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
The two factors need to be much closer.
(8)(-15) = -120 8 - 15 =
Tuesday, March 3, 2009
![Page 41: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/41.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
The two factors need to be much closer.
(8)(-15) = -120 8 - 15 = -7
Tuesday, March 3, 2009
![Page 42: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/42.jpg)
There is a pattern!First, multiply a and c.
(6)(-20) = -120Now, factor this product into two numbers that add up to b. Since b is negative, the larger factor must also be negative.
(2)(-60) = -120 2 - 60 = -58≠ -7
The two factors need to be much closer.
(8)(-15) = -120 8 - 15 = -7
GOOD NEWS!!!
Tuesday, March 3, 2009
![Page 43: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/43.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
Tuesday, March 3, 2009
![Page 44: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/44.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20
Tuesday, March 3, 2009
![Page 45: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/45.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
Tuesday, March 3, 2009
![Page 46: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/46.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Tuesday, March 3, 2009
![Page 47: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/47.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.
Tuesday, March 3, 2009
![Page 48: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/48.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m
Tuesday, March 3, 2009
![Page 49: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/49.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m
Tuesday, March 3, 2009
![Page 50: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/50.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4)
Tuesday, March 3, 2009
![Page 51: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/51.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5
Tuesday, March 3, 2009
![Page 52: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/52.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m
Tuesday, March 3, 2009
![Page 53: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/53.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m+ 4)
Tuesday, March 3, 2009
![Page 54: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/54.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m+ 4)
You will notice that the “stuff” inside the parentheses is the same. This is one of our factors. The “stuff” that’s left over
makes our other factor!
Tuesday, March 3, 2009
![Page 55: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/55.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m+ 4)
You will notice that the “stuff” inside the parentheses is the same. This is one of our factors. The “stuff” that’s left over
makes our other factor!
(3m + 4)
Tuesday, March 3, 2009
![Page 56: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/56.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m+ 4)
You will notice that the “stuff” inside the parentheses is the same. This is one of our factors. The “stuff” that’s left over
makes our other factor!
(3m + 4)(2m - 5)
Tuesday, March 3, 2009
![Page 57: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/57.jpg)
We’re going to take our quadratic and rewrite the middle term.
6m2 - 7m - 20
6m2 + 8m - 15m - 20Group the first two and last two terms (including minus signs).
(6m2 + 8m) + (- 15m - 20)
Factor out the GCF of each binomial.2m(3m + 4) - 5(3m+ 4)
You will notice that the “stuff” inside the parentheses is the same. This is one of our factors. The “stuff” that’s left over
makes our other factor!
(3m + 4)(2m - 5)
And we have our answer!Tuesday, March 3, 2009
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Process for factoring ax2 + bx + c
Tuesday, March 3, 2009
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Process for factoring ax2 + bx + c
1. Multiply a and c. Factor this number so that the two factors add up to b. (The larger factor will take the sign of b.)
Tuesday, March 3, 2009
![Page 60: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/60.jpg)
Process for factoring ax2 + bx + c
1. Multiply a and c. Factor this number so that the two factors add up to b. (The larger factor will take the sign of b.)
2. Group the first two and last two terms (including negative signs) and then factor out the GCF from each binomial.
Tuesday, March 3, 2009
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Process for factoring ax2 + bx + c
1. Multiply a and c. Factor this number so that the two factors add up to b. (The larger factor will take the sign of b.)
2. Group the first two and last two terms (including negative signs) and then factor out the GCF from each binomial.
3. Rewrite as the two factors: The “stuff” inside the parentheses is one, and the “stuff” outside is the other.
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Example 3: Factor.12x3 - 28x2 - 24x
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Tuesday, March 3, 2009
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
Tuesday, March 3, 2009
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -7
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)+ 2
Tuesday, March 3, 2009
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)+ 2(x - 3)]
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)+ 2(x - 3)]
4x[Tuesday, March 3, 2009
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)+ 2(x - 3)]
4x[(x - 3)Tuesday, March 3, 2009
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Example 3: Factor.12x3 - 28x2 - 24x
What do you do first?4x (3x2 - 7x - 6)
Is the quadratic factorable?b2 - 4ac = (-7)2 - 4(3)(-6) = 121
Okay, let’s do it!
(3)(-6) = -18 2 - 9 = -74x(3x2 - 7x - 6)
4x(3x2 - 9x + 2x - 6)4x[(3x2 - 9x) + (2x - 6)]4x[3x(x - 3)+ 2(x - 3)]
4x[(x - 3)(3x + 2)]Tuesday, March 3, 2009
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Example 4: Factor.
a. x2 + 5x + 6 b. x2 - 7x + 6
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Example 4: Factor.
a. x2 + 5x + 6 b. x2 - 7x + 6(1)(6) = 6
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Example 4: Factor.
a. x2 + 5x + 6 b. x2 - 7x + 6(1)(6) = 6
2 + 3 = 5
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Example 4: Factor.
a. x2 + 5x + 6
(x + 2)(x + 3)
b. x2 - 7x + 6(1)(6) = 6
2 + 3 = 5
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Example 4: Factor.
a. x2 + 5x + 6
(x + 2)(x + 3)
b. x2 - 7x + 6(1)(6) = 6
2 + 3 = 5
(1)(6) = 6
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Example 4: Factor.
a. x2 + 5x + 6
(x + 2)(x + 3)
b. x2 - 7x + 6(1)(6) = 6
2 + 3 = 5
(1)(6) = 6
-1 - 6 = -7
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Example 4: Factor.
a. x2 + 5x + 6
(x + 2)(x + 3)
b. x2 - 7x + 6
(x - 1)(x - 6)
(1)(6) = 6
2 + 3 = 5
(1)(6) = 6
-1 - 6 = -7
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
2x2 + 4x - 3x - 6
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
(x + 2)(2x - 3)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
(x + 2)(2x - 3)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
4x2 - 16x - 3x + 12
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
(x + 2)(2x - 3)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
4x2 - 16x - 3x + 12(4x2 - 16x) + (- 3x + 12)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
(x + 2)(2x - 3)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
4x2 - 16x - 3x + 12(4x2 - 16x) + (- 3x + 12)
4x(x - 4) - 3(x - 4)
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Example 5: Factor.a. 4x2 - 16x + 16 b. 25b4 - 81r8
c. 2x2 + x - 6 d. 4x2 - 19x + 12
4(x - 2)2 (5b2 - 9r4)(5b2 + 9r4)
(x + 2)(2x - 3)
2x2 + 4x - 3x - 6(2x2 + 4x) + (-3x - 6)2x(x + 2) - 3(x + 2)
4x2 - 16x - 3x + 12(4x2 - 16x) + (- 3x + 12)
4x(x - 4) - 3(x - 4)(x - 4)(4x - 3)
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 2
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
-1(6x2 + x - 2)
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
-1(6x2 + x - 2)-1(6x2 + 4x - 3x - 2)
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
-1(6x2 + x - 2)-1(6x2 + 4x - 3x - 2)
-[(6x2 + 4x) + (- 3x - 2)]
Tuesday, March 3, 2009
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e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
-1(6x2 + x - 2)-1(6x2 + 4x - 3x - 2)
-[(6x2 + 4x) + (- 3x - 2)]-[2x(3x + 2) -1(3x + 2)]
Tuesday, March 3, 2009
![Page 116: AA Section 11-3 Day 2](https://reader031.fdocuments.in/reader031/viewer/2022021816/548ffb74b479599b038b476a/html5/thumbnails/116.jpg)
e. 2x2 - 4x - 16 f. -6x2 - x + 22(x2 - 2x - 8)
2(x2 + 2x - 4x - 8)2[(x2 + 2x) + (-4x - 8)]2[x(x + 2) - 4(x + 2)]
2[(x + 2)(x - 4)]
-1(6x2 + x - 2)-1(6x2 + 4x - 3x - 2)
-[(6x2 + 4x) + (- 3x - 2)]-[2x(3x + 2) -1(3x + 2)]
-(3x + 2)(2x - 1)
Tuesday, March 3, 2009
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Homework
Tuesday, March 3, 2009
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Homework
You’ll know it when Mr. Lamb passes it out.
Tuesday, March 3, 2009