Question 1

Which of the following is the correct definition of the Greatest Common Factor (GCF) for a set of terms?

Accepted Answer

The largest expression that divides each term exactly, including variables.

Question 2

What is the GCF of $$12x^2y$ and 18xy^2$?

Accepted Answer

$$6xy$$

Question 3

Factor the following expression completely: $$25x^2 + 20x$

Accepted Answer

$$5x(5x + 4)$$

Question 4

Which of the following is the correct factorization by grouping for $$x^2 + 2x + x + 2$?

Accepted Answer

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

Question 5

What is the correct factorization of $$y^2 - 5y + 6$?

Accepted Answer

$$(y - 2)(y - 3)$$

Question 6

Which method is best for factoring $$3x^2 + 11x + 6$?

Accepted Answer

Trial and error (guess and check)

Question 7

Factor $$x^2 - 16$ using a special factoring technique.

Accepted Answer

$$(x + 4)(x - 4)$$

Question 8

Which of the following is the correct factorization for $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 9

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ using the zero-factor property.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 10

A participant book is 2 inches longer than it is wide. If the area of the cover is $$48$$ square inches, what is the width of the book?

Accepted Answer

$$6$$ inches

Question 11

Which of the following is the correct factorization for $$4x^2 - 9$?

Accepted Answer

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

Question 12

What is the correct factorization for $$x^2 + 6x + 9$?

Accepted Answer

$$(x + 3)^2$

Question 13

Which of the following is the correct factorization for $$x^2 - 10x + 25$?

Accepted Answer

$$(x - 5)^2$

Question 14

Solve for $$x in $$the equation $$3x(x - 2) = 0.$$

Accepted Answer

$$x = 0 or$$ $$x = 2$$

Question 15

If the hypotenuse of a right triangle is $$3 ft $$longer than the longer leg, and the shorter leg is $$3 ft $$shorter than the longer leg, what is the length of the longer leg?

Accepted Answer

$$12 ft$$

Question 16

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

Accepted Answer

$$(x + 4)(x - 2)$$

Question 17

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2 + 6x + 9$

Question 18

What is the correct factorization for $$x^3 + 27$?

Accepted Answer

$$(x + 3)(x^2$ - 3x + 9)$$

Question 19

Which of the following is the correct solution for the equation $$x^2 - 4x = 0$?

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Factoring and Applications: Study Guide for Intermediate Algebra

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