Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6)...
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Transcript of Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6)...
![Page 1: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/1.jpg)
Add or subtract
1. (x2 + 4x – 1) + (5x2 – 6x + 4)
2. (5y2 – 9y + 1) – (7y2 – 8y – 6)
Find the product
3. (x – 6)(3x + 4)
4. (2x + 5)(3x + 4)
6x2 – 2x + 3
-2y2 – y + 7
3x2 – 14x – 24
6x2 + 23x + 20
![Page 2: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/2.jpg)
# of Terms
Name by # of Terms
1 Monomial
2 Binomial
3 Trinomial
4+ Polynomial
![Page 3: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/3.jpg)
Degree(largest
exponent)
Name by degree
0 Constant
1 Linear
2 Quadratic
3 Cubic
![Page 4: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/4.jpg)
74 2z
Identify the polynomial by degree and by the number
of terms.
LinearBinomial
Degree:
# of Terms:
Leading Coefficient:74
![Page 5: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/5.jpg)
876 3r
Identify the polynomial by degree and by the number
of terms.
CubicMonomial
Degree:
# of Terms:
![Page 6: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/6.jpg)
25 7 2x x
Identify the polynomial by degree and by the number
of terms.
QuadraticTrinomial
Degree:
# of Terms:
Leading Coefficient:5
![Page 7: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/7.jpg)
Multiplying Polynomials
Binomial Theoremand
Pascal’s Triangle
![Page 8: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/8.jpg)
Pascal’s Triangle
1 n = 0
1 1 n = 1
1 2 1 n = 2
1 3 3 1 n = 3
??? n = 4
![Page 9: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/9.jpg)
Binomial Theorem 1 n = 0
1 1 n = 1
1 2 1 n = 2
1 3 3 1 n = 3(a+b)0 = 1
(a+b)1 = 1a + 1b
(a+b)2 = 1a2 + 2ab + 1b2
(a+b)3 = 1a3 + 3a2b + 3ab2
+ 1b3
![Page 10: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/10.jpg)
Binomial Theorem 1 n = 0
1 1 n = 1
1 2 1 n = 2
1 3 3 1 n = 3
Use the binomial theorem to write out (x + 3)2.
![Page 11: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/11.jpg)
Binomial Theorem 1 n = 0
1 1 n = 1
1 2 1 n = 2
1 3 3 1 n = 3
Use the binomial theorem to write out (x + 3)3.
![Page 12: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/12.jpg)
Binomial Theorem 1 n = 0
1 1 n = 1
1 2 1 n = 2
1 3 3 1 n = 3
Try (x + 2)4.
![Page 13: Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.](https://reader036.fdocuments.in/reader036/viewer/2022082917/5515824855034691418b5694/html5/thumbnails/13.jpg)
Application
x + 2
x + 2
Find an expression for the area of the base and then, the volume of the box:
A = x2 + 4x + 4
V = x3 + 6x2 + 12x + 8
x + 2