Question 1

Which of the following is the correct factorization of $x^2 + 14x + 45$?

Accepted Answer

$(x + 5)(x + 9)$

Question 2

What is the greatest common factor (GCF) of $4p^2 - 24p + 20$?

Accepted Answer

$4$

Question 3

After factoring out the GCF, what is the complete factorization of $4p^2 - 24p + 20$?

Accepted Answer

$4(p^2 - 6p + 5) = 4(p - 5)(p - 1)$

Question 4

Which of the following is the correct factorization of $2x^2 + 5x + 3$ using the 'Slip and Slide' method?

Accepted Answer

$(2x + 3)(x + 1)$

Question 5

A rectangular garden has an area represented by $2a^2 + 2a - 24$. What are the possible dimensions of the garden?

Accepted Answer

$(2a - 6)(a + 4)$

Question 6

Which of the following is the correct factorization of $3x^2 - 11x + 10$?

Accepted Answer

$(3x - 5)(x - 2)$

Question 7

A company’s profit can be modeled by $6x^2 + x - 12$. What is the correct factorization?

Accepted Answer

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

Question 8

Which of the following is the correct factorization of $9p^2 + 6p - 8$?

Accepted Answer

$(3p + 4)(3p - 2)$

Question 9

Given $10k^2 + 75k + 35$, what is the first step in factoring this trinomial?

Accepted Answer

Factor out the GCF, which is $5$

Question 10

Which of the following is the correct factorization of $10k^2 + 75k + 35$ after factoring out the GCF?

Accepted Answer

$5(2k + 1)(k + 7)$

Question 11

Which of the following is the correct factorization of $4a^2 - 4a + 1$?

Accepted Answer

$(2a - 1)^2$

Question 12

A quadratic expression $12x^2 + 2x - 2$ is used to model the area of a rectangle. What is its complete factorization?

Accepted Answer

$2(6x^2 + x - 1) = 2(3x - 1)(2x + 1)$

Question 13

Which of the following is the correct factorization of $15y^2 - 18y - 24$?

Accepted Answer

$3(5y + 4)(y - 2)$

Question 14

Which of the following is the correct factorization of $2k^2 - 11k + 15$?

Accepted Answer

$(2k - 5)(k - 3)$

Question 15

A company wants to design a rectangular billboard with an area given by $8x^2 - 2x - 10$. What is the correct factorization?

Accepted Answer

$2(4x + 5)(x - 1)$

Factoring Trinomials in College Algebra

Study Guide - Practice Questions