Question 1

Which of the following expressions is a perfect square trinomial?

Accepted Answer

$$x^2 + 14x + 49$

Question 2

Factor the expression $$36x^2 + 60x + 25$.

Accepted Answer

$$(6x + 5)^2$

Question 3

Which of the following is the correct factorization of $$49x^2 - 64$?

Accepted Answer

$$(7x + 8)(7x - 8)$$

Question 4

A rectangular garden has an area given by $$x^2 + 12x + 36$. What are the possible dimensions of the garden?

Accepted Answer

$$(x + 6) by$$ $$(x + 6)$$

Question 5

Which of the following expressions is NOT a difference of squares?

Accepted Answer

$$x^2 + 6x + 9$

Question 6

Factor $$a^2 - 10a + 25$ completely.

Accepted Answer

$$(a - 5)^2$

Question 7

Which formula is used to factor a perfect square trinomial?

Accepted Answer

$$a^2 + 2ab$$ + $$b^2 = (a$$ + $$b)^2$$

Question 8

Factor $$16x^2 - 24x + 9$.

Accepted Answer

$$(4x - 3)^2$

Question 9

A chemical reaction produces a compound whose mass is modeled by $$x^2 - 36$. What is the factorization of this expression?

Accepted Answer

$$(x + 6)(x - 6)$$

Question 10

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

Accepted Answer

$$(2x + 5)^2$

Question 11

Factor $$25a^2 - 36$ using the difference of squares formula.

Accepted Answer

$$(5a + 6)(5a - 6)$$

Question 12

Which of the following expressions is a difference of squares?

Accepted Answer

$$121x^2 - 49$

Question 13

Factor $$x^2 + 6x + 9$ completely.

Accepted Answer

$$(x + 3)^2$

Question 14

A company models its profit with $$9x^2 - 25$. What is the correct factorization?

Accepted Answer

$$(3x + 5)(3x - 5)$$

Question 15

Which of the following is the correct factorization for $$64a^2 - 81$?

Accepted Answer

$$(8a + 9)(8a - 9)$$

Question 16

Factor $$x^2 + 10x + 25$ completely.

Accepted Answer

$$(x + 5)^2$

Question 17

Which of the following is the correct factorization for $$x^2 - 8x + 16$?

Accepted Answer

$$(x - 4)^2$

Question 18

A medical researcher models the spread of a virus with $$x^2 - 49$. What is the correct factorization?

Accepted Answer

$$(x + 7)(x - 7)$$

Question 19

Which of the following is the correct factorization for $$x^2 + 12x + 36$?

Accepted Answer

$$(x + 6)^2$

Question 20

Factor $$121x^2 - 49$ using the difference of squares formula.

Accepted Answer

$$(11x + 7)(11x - 7)$$

Factoring Special Products: Perfect Squares and Difference of Squares

Study Guide - Practice Questions