Unit 7: Factoring Review

Factoring trinomials

100

Factor: x²+10x+25

(x+5)(x+5)

200

Factor: x²-12x+27

(x-9)(x-3)

300

If the equation: x² + 2x - 24 = (x + a)(x - b). What are the values of a and b?

a = 6 and b = 4

400

Factor: x² + 17x - 60

(x- 3)(x + 20)

500

Factor: 2x²-7x+6

(2x-3)(x-2)

Polynomials

100

Determine the sum of (x² + 7x - 8) and (6x² - 13x + 9)

7x² - 6x + 1

200

Determine the difference:

(x² + 7x - 8) - (6x² - 13x + 9)

-5x² + 20x - 17

300

Write a trinomial that meets the following criteria:

1. Degree of 2 

2. Leading coefficient of 7

3. Constant term of -4

4. In Standard Form

Answers will vary

400

Simplify the expression: 3(x² − 1) − (x² − 7x + 10) and write it in its standard form.

2x² + 7x - 13

500

Determine the area of a rectangle that has a length of (3x - 6) and a width of (7x + 4)

21x² - 30x - 24 

Factor GCF and Factoring Completely

100

What is the GCF of 

3x² - 12x?

3x

200

Factor: 6x² - 24x

6x(x - 4)

300

Factor using GCF: 3x³ - 15x² + 24x

3x(x² - 5x + 8)

400

When factored completely, 

x³ – 13x² – 30x is

x(x - 15)(x + 2)

500

When factored completely: 

16y⁴ - 64y² is

16y²(y - 2)(y + 2)

Mixed Review

100

Determine the value of f(3) given f(n) = 6n - 18

f(3) = 0

200

Solve the equation below for y:

3y - 10 = 5y + 50 

y = -30

300

A plumber has a set fee for a house call and charges by the hour for repairs. The total cost of her services can be modeled by c(t) = 125t + 95. Which statements about this function are true? 

I. A house call fee costs $95. 

II. The plumber charges $125 per hour. 

III. The number of hours the job takes is represented by t. 

1) I and II, only 

2) I and III, only 

3) II and III, only 

4) I, II, and III

Choice 4

(DOTS) Factoring the difference of two perfect squares

100

Factor: x²-16

(x+4)(x-4)

200

Factor: 9-x²

(3+x)(3-x)

300

Factor: 25y²-4

(5y+2)(5y-2)

400

Factor: 4x² - 169

(2x - 13)(2x + 13)

500

100x² - 144y²

(10x - 12y)(10x + 12y)