Question 1

Which of the following is the correct factorization of $3x + 12$?

Accepted Answer

$3(x + 4)$

Question 2

What is the greatest common factor (GCF) of $12y^2 - 18y$?

Accepted Answer

$6y$

Question 3

Factor $14x^3y^2 - 28x^2y^3$ completely.

Accepted Answer

$7x^2y^2(2x - 4y)$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

Difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Question 6

Factor $x^2 + 7x + 10$ completely.

Accepted Answer

$(x + 5)(x + 2)$

Question 7

Which of the following is the correct factorization of $3x^2 + x - 4$?

Accepted Answer

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

Question 8

A chemical reaction produces a polynomial $4x^5 - 36x^3 - 4x^2 + 36$. Factor it completely.

Accepted Answer

$4(x^2 - 9)(x^3 - 1)$

Question 9

Which of the following is the correct factorization of $49a^2b + 10ab^3 + 6ab^2$?

Question 10

A factory produces objects whose area is modeled by $x^2 - 7x + 10$. What are the possible dimensions?

Accepted Answer

$(x - 5)$ and $(x - 2)$

Question 11

Which of the following is the correct factorization of $20x^2 - 45y^2$?

Accepted Answer

$5(4x^2 - 9y^2)$

Question 12

Which of the following is the correct factorization of $27u^3 + 8$?

Accepted Answer

$(3u + 2)(9u^2 - 6u + 4)$

Question 13

A medical researcher models the growth of bacteria with $x^3 + y^3$. Which formula should be used to factor this expression?

Accepted Answer

Sum of cubes: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

Question 14

Factor $2x^3 - 10x^2 + 8x$ completely.

Accepted Answer

$2x(x^2 - 5x + 4)$

Question 15

A company wants to factor $4m^2 + 3m - 12$ to determine the dimensions of a rectangular plot. What is the correct factorization?

Accepted Answer

$(4m + 3)(m - 4)$

Question 16

Which of the following is the correct factorization of $x^4 + x^3 + x^2$?

Accepted Answer

$x^2(x^2 + x + 1)$

Question 17

Which of the following is the correct factorization of $x^2 - 3x - 4$?

Accepted Answer

$(x - 4)(x + 1)$

Question 18

A biologist is studying a population modeled by $x^3 - 1$. What is the correct factorization?

Accepted Answer

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

Question 19

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

Accepted Answer

$(x - 4)(x - 5)$

Factoring Polynomials in College Algebra: Methods and Applications

Study Guide - Practice Questions