Question 1

Which of the following polynomials is a difference of squares and can be factored using the formula $a^2 - b^2 = (a + b)(a - b)$?

Accepted Answer

$9a^2 - 121$

Question 2

Factor the expression $16y^2 - 25$ completely.

Accepted Answer

$(4y + 5)(4y - 5)$

Question 3

A rectangular garden has an area represented by $x^2 - 36$ square meters. What are the possible dimensions of the garden in terms of $x$?

Accepted Answer

$(x + 6)$ meters and $(x - 6)$ meters

Question 4

Which of the following is the correct factorization of $81n^4 - 25$?

Accepted Answer

$(9n^2 + 5)(9n^2 - 5)$

Question 5

Given $18x^2 - 50$, what is the first step in factoring this expression?

Accepted Answer

Factor out the greatest common factor (GCF), which is $2$

Question 6

After factoring out the GCF, completely factor $32s^2 - 18u^2$.

Accepted Answer

$2(4s + 3u)(4s - 3u)$

Question 7

Which of the following polynomials is PRIME (cannot be factored over the real numbers)?

Accepted Answer

$k^2 + 25$

Question 8

A company is designing a square logo with an area of $a^2 - 4$ square inches. What are the possible side lengths of the logo?

Accepted Answer

$(a + 2)$ inches and $(a - 2)$ inches

Question 9

Factor $4h^2 - 25g^2$ completely.

Accepted Answer

$(2h + 5g)(2h - 5g)$

Question 10

Which of the following is the correct factorization of $49m^4 - 16$?

Accepted Answer

$(7m^2 + 4)(7m^2 - 4)$

Question 11

A physics equation involves the expression $x^2y^2 - 1$. Factor this expression completely.

Accepted Answer

$(xy + 1)(xy - 1)$

Question 12

Factor $3p^2 - 75$ completely.

Accepted Answer

$3(p + 5)(p - 5)$

Question 13

Which of the following is the correct factorization of $121r^6 - 1$?

Accepted Answer

$(11r^3 + 1)(11r^3 - 1)$

Question 14

A biologist is studying the area difference between two square petri dishes, one with side $2a$ and the other with side $3b$. Express the difference in their areas and factor it completely.

Accepted Answer

$(2a + 3b)(2a - 3b)$

Question 15

Factor $8x^2y - 32y^3$ completely.

Accepted Answer

$8y(x + 2y)(x - 2y)$

Question 16

Which of the following is the correct factorization of $m^2 - 64n^2$?

Accepted Answer

$(m + 8n)(m - 8n)$

Question 17

Factor $4p^4 - 25$ completely.

Accepted Answer

$(2p^2 + 5)(2p^2 - 5)$

Question 18

A chemist is comparing the difference in the squares of two concentrations, $a^2b^2 - 100$. Factor this expression completely.

Accepted Answer

$(ab + 10)(ab - 10)$

Question 19

Which of the following is the correct factorization of $36c^2 - d^2$?

Accepted Answer

$(6c + d)(6c - d)$

Question 20

Factor $81m^4 - m^2$ completely.

Accepted Answer

$m^2(9m + 1)(9m - 1)$

Factoring and Simplifying Polynomials: Difference of Squares & GCF

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