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

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