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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