Question 1

Which of the following is the correct factorization of $$4a^2 + 8a$?

Accepted Answer

$$4a(a + 2)$$

Question 2

A chemist is mixing two solutions. The total cost in dollars of the chemicals is modeled by the polynomial $$2x^2 + 6x$. Factor this expression to find the greatest common factor (GCF).

Accepted Answer

$$2x(x + 3)$$

Question 3

Which of the following is the correct factorization of $$3x^2 - 5x$?

Accepted Answer

$$x(3x - 5)$$

Question 4

A rectangular garden has an area given by $$2n^2 + 3n - 9$ square meters. Which of the following is the correct factorization of this area?

Accepted Answer

$$(2n - 3)(n + 3)$$

Question 5

Which of the following is the correct factorization of $$k^2 - 13k + 40$?

Accepted Answer

$$(k - 5)(k - 8)$$

Question 6

A company’s profit, in thousands of dollars, is modeled by $$6x^2 + 37x + 6$. Which of the following is the correct factorization?

Accepted Answer

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

Question 7

Which of the following is the correct factorization of $$a^2 - a - 90$?

Accepted Answer

$$(a - 10)(a + 9)$$

Question 8

A quadratic equation is given by $$(x - 3)(2x + 1) = 0. $$What are the solutions to this equation?

Accepted Answer

$$x = 3$$ and $$x = -\frac{1}{2}$$

Question 9

Which of the following is the correct factorization of $$4n^2 - 15n - 25$?

Accepted Answer

$$(n - 5)(4n + 5)$$

Question 10

A rectangular field has an area of $$15n^2 - 27n - 6$ square meters. Which of the following is the correct factorization?

Accepted Answer

$$3(5n + 1)(n - 2)$$

Question 11

Which of the following is the correct factorization of $$b^2 + 16b + 64$?

Accepted Answer

$$(b + 8)^2$

Question 12

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

Accepted Answer

$$(2n + 1)(n + 2)$$

Question 13

A quadratic equation $$x^2 - 16x + 64 = 0$ is solved by Mrs. Meo, who finds x = 8$. Is this correct, and why?

Accepted Answer

Yes, because $$x^2 - 16x + 64 = (x$$ - $$8)^2$$, so $$x = 8 is $$the only solution.

Question 14

Which of the following is the correct factorization of $$6x^2 + 7x - 49$?

Accepted Answer

$$(3x - 7)(2x + 7)$$

Question 15

Which of the following is the correct factorization of $$x^2 - 15x + 50$?

Accepted Answer

$$(x - 10)(x - 5)$$

Question 16

A quadratic equation is given by $$2n^2 + 6n - 108 = 0$. What are the solutions to this equation?

Accepted Answer

$$n = -9$$ and $$n = 6$$

Question 17

Which of the following is the correct factorization of $$4x^2 - 35x + 49$?

Accepted Answer

$$(x - 7)(4x - 7)$$

Question 18

Which of the following is the correct factorization of $$16b^2 + 60b - 100$?

Accepted Answer

$$4(b + 5)(4b - 5)$$

Question 19

What is always a good first step when solving quadratic equations by factoring?

Accepted Answer

Set the equation equal to zero.

Factoring and Quadratic Equations – Step-by-Step Algebra 1 Guidance

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