Chapter 8: Polynomials

Adding/Subtracting

100

Add: (4x² + 9x + 1) + (2x² + 7x + 13)

6x² + 16 x + 14

200

Subtract: (8x² + 5x + 7) - (5x² + 8x - 6)

3x² - 3x + 13

300

Subtract: (5x⁴ + 7x + 2) - (3x² - 2x + 9)

5x⁴ -3x² + 9x -7

400

Add: (-7x³ + 4x - 6) + (6x³ + 10x² + 3)

-x³ + 10x² + 4x - 3

500

Simplify: (5x+2)(x+4) – (3x² - 4x + 17)

2x² + 26x - 9

Multiplying/GCF

100

Find the greatest common factor: 16x⁶ + 22x² + 30x⁵

2x²

200

Find the greatest common factor: 7v³ – 10v² + 9v⁴

v²

300

Multiply: -p (8p² + 3p)

-8p³ - 3p²

400

Multiply: 4m (3m + 9m² – 6)

36m³ + 12m² - 24m

500

Multiply: 7m²n (3m + 4n³ + 6)

28m²n⁴ + 21m³n + 42m²n

Multiplying polynomials

100

What is the product of 2x² and (4x+8)

8x³ + 16x²

200

FOIL: (5w – 6) (2w +7)

10w² + 23w - 42

300

Simplify: (y – 6) (3y + 7)

3y² - 11y - 42

400

Simplify: (4n³ + 3) (3n + 5) 

12n⁴ + 20n³ + 9n + 15

500

Multiply: (4s² + 3s + 5) (7s – 3)

28s³ + 9s² + 19s - 15

Factoring

100

Factor: x² + 17x + 72

(x + 9) (x + 8)

200

Factor: 4v² – 16v + 7

(2v - 7) (2v - 1)

300

Factor: 7n⁴ – 4n³ + 28n² - 16n

n (7n - 4) (n² + 4)

400

Factor: 15t³ + 2t² – 45t – 6

(t² - 3) (15t + 2)

500

Factor: 5g² + 15gh + 10h²

5 (g + 2h) (g + h)

Special Cases

100

Simplify: (q – 1)²

q² - 2q + 1

200

Simplify: (3g – 5) (3g + 5)

9g² - 25

300

Factor: n² – 16n + 64

(n - 8)²

400

Factor: y² – 121

(y + 11) (y - 11)

500

Factor: 32v² – 8

8 (2v - 1) (2v + 1)