Rational Exponents Lesson 6.4 Algebra II HW: 6.4/10-66 multiples of 3.
Algebra 2: Section 6.4
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Transcript of Algebra 2: Section 6.4
![Page 1: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/1.jpg)
Algebra 2: Section 6.4
Factoring and Solving Polynomial Equations
![Page 2: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/2.jpg)
Factoring Quadratics
1. 4x2 24x
4x(x 6)
Common Factor: 4x
![Page 3: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/3.jpg)
Factoring Quadratics
2. 2x2 11x 21
(2x_____)(x_____)
Two factors of -21 that when
FOI LED make the middle
term +11
(2x 3)(x 7)
![Page 4: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/4.jpg)
Factoring Quadratics
23. 4x 36 81x
(2x)2 2 2x 9 (9)2
(2x 9)2
Perfect Square Trinomial
![Page 5: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/5.jpg)
Sum and Difference of Cubes
a3 b3 (a b)(a2 ab b2)
a3 b3 (a b)(a2 ab b2)
x3 64 (x 4)(x2 4x 16)
27x3 8 (3x 2)(9x2 6x 4)
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Examples
4. 125 x3
x3 53
(x 5)(x2 5x 52)
(x 5)(x2 5x 25)
Rewrite as sum of cubes
(Changed order, standard)
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Factoring by Grouping(used when there are 4 terms)
• Factor common factor out of first two terms
and factor another common factor out of last
two terms
(may need to rearrange)
• Factor common binomial out of each ‘term’
![Page 8: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/8.jpg)
Examples
5. x2y2 3x2 4y2 12
x2(y2 3) 4(y2 3)
(y2 3)(x2 4)
(y2 3)(x 2)(x 2)
Difference of two squares
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Examples2 2 3 46. a 8 16b ab b
b2(a2 8ab 16b2)
b2(a 4b)(a 4b)
b2(a 4b)2
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Examples47. 25x 36
(5x2)2 (6)2
Difference of two squares
(5x2 6)(5x2 6)
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W hich method of factoring?
• 2 terms
• 3 terms
• 4 terms
• Diff. of Squares
• Sum or Diff. of Cubes
• Trial and Error
• Perfect Square Trinomial
• Grouping
Always look for common
factor!!
![Page 12: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/12.jpg)
Solving Polynomial Equations by
Factoring
(Examples)58. 2 18 0y y
42 ( 9) 0y y2 22 ( 3)( 3) 0y y y
Difference of two squares
2 22 0 3 0 3 0y or y or y
0 3 3y or y or y i
0 3y or yFor this assignment,
only concerned with
real solut ions
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More Examples5 29. 4 108 0x x
2 34 ( 27) 0x x2 24 ( 3)( 3 9) 0x x x x
Difference of two cubes
2 24 0 3 0 3 9 0x or x or x x
3 9 4(1)(9)0 3
2x or x or x
0 3x or xThis is going to be
imaginary.
The discriminant is
negative!
![Page 14: Algebra 2: Section 6.4](https://reader031.fdocuments.in/reader031/viewer/2022013110/546a9fc8b4af9f7a2c8b47ca/html5/thumbnails/14.jpg)
Assignment
• p.349
# 33-85 all, 87, 88
(55 problems)
• Due W ednesday!