Factoring Polynomials

Monomials

100

Find the GCF of each pair of monomials. 

12ab and 12

12

200

Find the GCF of each pair of monomials. 

3e⁵ and 9e²

3e²

300

Find the GCF of each pair of monomials 

-8b³ and 14b⁴

2b³

400

Factor each polynomial. 

8c²+7c

c(8c+7)

500

Factor each polynomial. 

15x⁵ - 18x

3x(5x⁴ -6)

Common Binomials

100

Find the GCF for each pair of expressions.

5(x-3) and 25(x-3)² 

5(x-3)

200

Find the GCF for each pair of expressions. 

12(a-4)⁵ and 2(a-4)⁴

2(a-4)⁴

300

Find the GCF for each pair of expressions. 

-7(z-9)⁸ and 14(z-9)²

7(z-9)²

400

Find the GCF for each pair of expressions. 

-4(a-2), 12(a-2)⁵, and 20(a-2)³

4(a-2)

500

Edwin was taking a quiz and factoring monomials. Exercise 5 asked her to find the GCF of 18a³b⁴ and 27a⁵b². She gave an answer of 6a⁵b⁴. Is this correct? If not give the correct answer. 

No; 9a³b²

x^2+bx+c

100

Fill in the blank to factor the polynomial.

t² +6t+5 = (t+5)(t+___)

1

200

Fill in the blank to factor the polynomial. 

x² - 4 = (x+2)(x-___)

2

300

Factor the polynomial completely. 

z² - 7z+12

(z-4)(z-3)

400

Fill in the blank to factor the polynomial. 

-x² - 7x -6

-(x+6)(x+1)

500

Factor the polynomial. 

n² - 25

(n+5)(n-5)

ax^2+bx+c

100

Factor the polynomial completely. 

2x²+13x+15

(2x+3)(x+5)

200

Factor the polynomial completely. 

3x²+10x+8

(3x+4)(x+2)

300

Factor the polynomial completely. 

5x²+21x+4

(5x+1)(x+4)

400

Factor the polynomial completely. 

*Hint: Factor out -1. 

-2x²+5x+42

-1(2x+7)(x-6)

500

The area of a rectangle is 20x²-27x-8. The length is 4x+1. What is the width?

5x-8

Word Problems

100

The perimeter of a rhombus is 12x +28 feet. 

a) Factor the expression. 

b) The find the length of one side if x=8. 

*Hint: A rhombus is a parallelogram with four congruent sides. 

a) 4(3x+7)

b) 31 feet

200

A teacher is writing a test on factoring. The teacher wants students to find the GCF of 45x⁴y⁸, 120x²y⁵, and 75x⁶y⁴. What is the correct answer. 

a) 15x²y⁴

b) 15x⁶y⁸

c) 45x²y⁴

d) 75x⁶y⁴

a) 15x²y⁴

300

A plot of land is rectangular and has an area of 

x²-5x-24 meters squared. The length is x + 3 meters. Find the width of the plot. 

Width: x - 8

400

The area of a rug which is shaped like a rectangle is 4x²+4x square feet. Factor this polynomial to expressions for the dimensions of the rug. 

Factor: 4x(x+1)

Dimensions: 4x and x +1

500

For a certain college, the number of applications received after x recruiting seminars is modeled by the polynomial 3x²+490x+6000. What is the expression in factored form. 

a) (3x-40)(x-150)

b (3x+40)(x+150)

c) (3x-30)(x-200)

d (3x-30)(x+200)

b) (3x+40)(x+150)