Question 1

Which of the following is the correct factorization of $$4x^2 + 7x + 3$?

Accepted Answer

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

Question 2

Given $$6x^2 + x - 2$, which pair of binomials correctly factors the expression?

Accepted Answer

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

Question 3

What is the result of factoring $$10x^2 - 19x + 6$?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

If $$a^2$$ - $$b^2 is $$factored, which of the following is correct?

Accepted Answer

$$(a-b)(a+b)$$

Question 6

Which of the following is the correct factorization of $$4x^2 + 20mn$$ + $$25n^2$$?

Accepted Answer

$$(2x+5n)^2$$

Question 7

A chemical reaction produces a quadratic equation $$x^2 - 16 = 0$ for the concentration of a reactant. What are the possible concentrations?

Accepted Answer

$$x = 4 or$$ $$x = -4$$

Question 8

Which of the following is the correct factorization of $$y^2 - 56y + 784$?

Accepted Answer

$$(y-28)^2$$

Question 9

A rectangular garden has an area given by $$x^2 + 7x + 12$. What are the possible integer dimensions of the garden?

Accepted Answer

$$(x+3)$$ and $$(x+4)$$

Question 10

Which of the following is the correct factorization of $$9p^2 - 60p + 100$?

Accepted Answer

$$(3p-10)^2$$

Question 11

A physics problem gives the equation $$x^2$$ - $$25y^2 = 0$ for the displacement of a spring. What is the correct factorization?

Accepted Answer

$$(x-5y)(x+5y)$$

Question 12

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

Accepted Answer

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

Question 13

A quadratic equation $$x^2 - 2x - 15 = 0$ models the profit of a business. What are the break-even points?

Accepted Answer

$$x = 5$$ and $$x = -3$$

Question 14

Which of the following is the correct factorization of $$a^2 + 2ab$$ + $$b^2$$?

Accepted Answer

$$(a+b)^2$$

Question 15

A projectile's height is modeled by $$x^2 - 49$. What are the possible heights where the projectile crosses the ground?

Accepted Answer

$$x = 7$$ and $$x = -7$$

Question 16

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

Accepted Answer

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

Question 17

If $$a^2 - 2ab$$ + $$b^2 is $$factored, which of the following is correct?

Accepted Answer

$$(a-b)^2$$

Question 18

Which of the following is the correct factorization of $$x^2 - 81$?

Accepted Answer

$$(x-9)(x+9)$$

Question 19

A quadratic equation $$x^2 + 6x + 9 = 0$ is given. What is the correct factorization?

Accepted Answer

$$(x+3)^2$$

Question 20

Which of the following is the correct factorization of $$y^2 - 100$?

Accepted Answer

$$(y-10)(y+10)$$

Factoring Polynomials: Methods and Applications

Study Guide - Practice Questions