Unit 4 Test Review

Factoring

100

Factor the following completely
x²+8x+12

(x+6)(x+2)

200

Factor the following completely
4x² + 32x + 64

4 (x + 4) (x + 4)

300

Factor the following completely
4x² - 49

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

400

Factor the following completely
6x² - 11x + 4

(3x - 4)(2x - 1)

500

Factor the following completely
x⁴ - 1

(x-1)(x+1)(x^2+1)

Quadratic Formula

100

Solve using the quadratic formula:
x² - 5x + 6 = 0

x = 2 and x = 3

200

Solve using the quadratic formula:
x² - 4x - 1 = 0

x = 2 + sqrt(5) and x = 2 - sqrt(5)

300

Solve using the quadratic formula
2x² + 3x = 5

x = 1 and x = -5/2

400

Solve using the quadratic formula
x² = -2x - 5

x = -1 +2i and x = -1 - 2i

500

Solve using the quadratic formula
3x² + 4x + 6 = 0

x = (-2 + i sqrt(14))/3 and x = (-2 - i sqrt(14))/3

Complete the Square

100

Find the value of "c" that would make this a perfect square trinomial

x² - 18x + c

c = 81

200

Solve by completing the square
x² + 6x + 5 = 0

x = -1 and x = -5

300

Solve by completing the square
x² - 16x + 2 = 0

x = 8 + sqrt(62) and x = 8 - sqrt(62)

400

Solve by completing the square
x² + 4x + 8 = 0

x = -2 + 2i and x = -2 - 2i

500

Solve by completing the square
2x² + 8x = -3

x = -2 + sqrt(5/2) and x = -2 - sqrt(5/2)

Square Roots

100

Simplify sqrt(20)

2sqrt(5)

200

Simplify sqrt(72)

6sqrt(2)

300

Simplify sqrt(-120)

2isqrt(30)

400

Solve using the square root property
x² + 11 = 36

x = 5 and x = -5

500

Solve using the square root property
5(x + 4)² - 3 = 12

x = -4 + sqrt(3) and x = -4 - sqrt(3)

Miscellaneous

100

Factor by GCF
10a³b⁴-6a²b⁶

2a²b⁴(5a³-3b²)

200

Write as a binomial squared
x² - 10x + 25

(x - 5)²

300

Solve the following equation by factoring
2x² + 7x + 3 = 0

x = -1/2 and x = -3

400

Simplify completely
sqrt(5)/sqrt(3)

sqrt(15)/3

500

Factor completely
2x² + 6x - xy - 3y

(x + 3)(2x - y)