Question 1

Which of the following is the correct factorization of $$9y^2 - 16$?

Accepted Answer

$$(3y - 4)(3y + 4)$$

Question 2

What is the greatest common factor (GCF) of $$-8x^2 + 24x$?

Accepted Answer

$$-8x$$

Question 3

Which of the following is the correct factorization of $$x^2 + 9x + 20$?

Accepted Answer

$$(x + 4)(x + 5)$$

Question 4

Given $$x^3 - 27$, which formula should be used to factor it completely?

Accepted Answer

Difference of cubes

Question 5

What is the complete factorization of $$x^3 - 27$?

Accepted Answer

$$(x - 3)(x^2$ + 3x + 9)$$

Question 6

Which acronym helps you remember the signs when factoring the sum or difference of cubes?

Accepted Answer

SOAP

Question 7

What is the correct factorization of $$6x^2 - 18x - 60$?

Accepted Answer

$$6(x - 5)(x + 2)$$

Question 8

Which of the following is the correct factorization of $$x^2 - 1$?

Accepted Answer

$$(x - 1)(x + 1)$$

Question 9

A trinomial $$ax^2 + bx + c$ can be factored by reversing which process?

Accepted Answer

FOIL

Question 10

What is the complete factorization of $$x^3 + 27$?

Accepted Answer

$$(x + 3)(x^2$ - 3x + 9)$$

Question 11

Which of the following is the correct factorization of $$3x^2 - 75$?

Accepted Answer

$$3(x - 5)(x + 5)$$

Question 12

What is the greatest common factor (GCF) of $$18m^3$$ + $$3m^2 - 6m$?

Accepted Answer

$$3m$$

Question 13

Which of the following is the correct factorization of $$x^2 + 7x + 12$?

Accepted Answer

$$(x + 3)(x + 4)$$

Question 14

Which of the following is the correct factorization of $$x^3 - 125$?

Accepted Answer

$$(x - 5)(x^2$ + 5x + 25)$$

Question 15

Which of the following is the correct factorization of $$144x^2 + 121$?

Accepted Answer

Cannot be factored over the real numbers

Question 16

What is the correct factorization of $$x^2 - 64$?

Accepted Answer

$$(x - 8)(x + 8)$$

Question 17

Which of the following is the correct factorization of $$6x^2 - 11x + 4$?

Accepted Answer

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

Question 18

Which of the following is the correct factorization of $$x^3 + 8$?

Accepted Answer

$$(x + 2)(x^2$ - 2x + 4)$$

Question 19

Which of the following is the correct factorization of $$12x^2 - 8x$?

Accepted Answer

$$4x(3x - 2)$$

Factoring Polynomials: A Study Guide for College Algebra

Study Guide - Practice Questions