Question 1

Which of the following is the correct first step when factoring the trinomial $$6x^2 + 9x + 3$?

Accepted Answer

Factor out the GCF, which is $$3$$

Question 2

What is the factored form of $$3x^2 + 10x + 8$?

Accepted Answer

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

Question 3

A chemist is mixing two solutions. The total cost in dollars of producing $$x$$ liters is modeled by $$4x^2 + 20x + 24$. What is the completely factored form of this expression?

Accepted Answer

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

Question 4

Which of the following trinomials requires factoring out a GCF before using the AC method?

Accepted Answer

$$8x^2 + 20x + 12$

Question 5

Factor completely: $$6x^2 + 12x + 6$

Accepted Answer

$$6(x + 1)(x + 1)$$

Question 6

A rectangular garden has an area given by $$2x^2 + 5x + 3$ square meters. What are the possible integer dimensions of the garden?

Accepted Answer

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

Question 7

Which of the following is the correct factorization of $$9x^2 + 12x + 4$?

Accepted Answer

$$(3x + 2)^2$

Question 8

A company’s profit, in thousands of dollars, is modeled by $$5x^2 + 10x + 5$. What is the completely factored form of this expression?

Accepted Answer

$$5(x + 1)^2$

Question 9

Which step is NOT part of the AC method for factoring $$ax^2 + bx + c$?

Accepted Answer

Divide all terms by $$a$$

Question 10

Factor completely: $$8x^2 + 20x + 12$

Accepted Answer

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

Question 11

A medical researcher models the number of bacteria in a culture as $$3x^2 + 14x + 8$. What is the factored form of this expression?

Accepted Answer

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

Question 12

Which of the following is the correct factorization of $$12x^2 + 18x + 6$?

Accepted Answer

$$6(2x + 1)(x + 1)$$

Question 13

A student factors $$4x^2 + 24x + 32$ as 4(x^2$ + 6x + 8). $$What is the next step to factor completely?

Accepted Answer

Factor $$x^2 + 6x + 8$ as (x + 2)(x + 4$$)$$

Question 14

Factor completely: $$10x^2 + 25x + 15$

Accepted Answer

$$5(2x + 3)(x + 1)$$

Question 15

Which of the following is the correct factorization of $$2x^2 + 7x + 3$?

Accepted Answer

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

Question 16

A business’s revenue is modeled by $$6x^2 + 17x + 5$. What is the factored form of this expression?

Accepted Answer

$$(3x + 5)(2x + 1)$$

Question 17

Which of the following is the correct factorization of $$5x^2 + 9x + 4$?

Accepted Answer

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

Question 18

A student is asked to factor $$6x^2 + 11x + 3$. Which two numbers should they find that multiply to a$$ \cdot c$$ and add to b$?

Accepted Answer

$$2$$ and $$9$$

Question 19

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

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

Factoring Trinomials and Using the Greatest Common Factor (GCF)

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