Ch.8 - Polynomials

Factor Completely!

100

Factor out the GCF

12x²y² + 4x³y + 8x²y

4x²y(3y + x + 2)

200

15x³ + 40x² + 3x + 8 

(5x² + 1)(3x + 8)

300

8y³ - 32y² + 28y - 112 

4(2y² + 7)(y - 4)

400

A trunk in the shape of a rectangular prism has a volume of 6w³ + 38w² - 28w.  What expressions can represent the dimensions of the trunk?

2w(w + 7)(3w - 2)

500

66x² + 57x + 12

3(11x+4)(2x+1)

Adding or Subtracting Polynomials

100

(2x²+3x-5) + (-7x²+4x+1)

-5x² + 7x - 4 

200

(x²-6x+7) - (2x²+x+6)

-x²-7x+1

300

(5x-7) - (2x²+8x-2)

-2x² - 3x - 5

400

(5x-3) + (4x+7) - (2x-6)

7x + 10

500

(2x²-6x-8) - (2x²-6x+8)

-16

Factoring Polynomials

100

y² + 15y + 56

(y + 8)(y + 7)

200

x² - 18x - 63

(x - 21)(x + 3)

300

6x² + 7x - 5

(3x + 5) (2x - 1)

400

2x² - 13x - 24

(2x + 3)(x - 8)

500

4x² - 4x - 35

(2x+5)(2x-7)

Multiplying Polynomials

100

4x(7x²+x+12)

28x³+4x²+48x

200

-3x(6x²-3x+8)

-18x³+9x²-24x

300

(5x-2)(x+3)

5x² + 13x - 6

400

(9x+4)(5x-3)

45x² - 7x -12

500

(2x+7)(3x²-5x+2)

6x³ + 11x² - 31x + 14

Special Cases

100

(x + 5)²

x² + 10x + 25

200

(x + 6)(x - 6)

x² - 36

300

The area of a square painting is x² + 18x + 81.  What is the side length of the painting?

(x + 9)

400

36x² - 60x + 25

(6x - 5)²

500

9x² - 196

(3x + 14)(3x - 14)