Algebra Unit 7 Polynomials and Factoring Review

Adding and Subtracting

100

Simplify –6ab + 3ab – b

–3ab – b

200

Simplify (3x² + 5) + (16x² + 7)

19x² + 12

300

Simplify (11n – 4) – (5n + 2) 

6n - 6

400

3d² + 8d – 2 – (6 + 2d² – 7d)

d² + 15d – 8

500

The fence around a quadrilateral-shaped pasture is (3a² + 15a + 9) feet long. Three sides of the fence have the following lengths: 5a, 10a – 2, a² – 7. What is the length of the fourth side of the fence?

2a² +18 feet

Multiplying and Factoring GCF

100

Simplify 2x(x + 8)

2x² + 16x

200

Find the GCF of 4x³ + 24x

4x

300

Write the factored form of the polynomial 4t³ + 24t² – 12t

4t(t² + 6t – 3)

400

Classify this polynomial by degree and number of terms.

-3x² + 8x - 5

Quadratic trinomial

500

Write the factored form of the polynomial

2x⁶y⁴ – 8x³y² + 14x⁴

2x³(x³y⁴ – 4y² + 7x)

Binomials & Special Cases

100

Multiply (y – 4)(y + 7)

y² + 3y – 28

200

Multiply (3x + 1)(5x – 3)

15x² – 4x – 3

300

Multiply (x + 3)(x² – 2x + 4)

x³ + x² - 2x + 12

400

Multiply (5x + 2)²

25x² +20x + 4

500

Multiply (30x + 17)(30x – 17)

900x² – 289

Factoring Trinomials a=1

100

Factor x² – 16x + 63

(x – 9)(x – 7)

200

Factor q² + 12q + 20

(q + 2)(q + 10)

300

Factor a² – 7a – 18

(a – 9)(a +2)

400

Factor x² + 5x – 14

(x + 7)(x – 2)

500

Factor k² + 4k – 96

(k + 12)(k – 8)

Factoring Trinomials a>1

100

Factor 2w² + 13w + 15

(2w + 3)(w + 5)

200

Factor 3d² + 20d + 12

(3d + 2)(d + 6)

300

Factor 6r² – 10r – 24

2(3r + 4)(r – 3)

400

Factor 3x² + 9x – 84

3(x + 7)(x – 4)

500

Factor 24c² + 96c + 90

6(2c + 5)(2c + 3)