Question 1

Which of the following is the complete factorization of $$3x^2 + 6x - 45$?

Accepted Answer

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

Question 2

Factor completely: $$x(x^2 - 49$$)$$

Accepted Answer

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

Question 3

Simplify the expression: $$(2x^3)(3x^2$)(4x^2$$)$$

Accepted Answer

$$24x^7$$

Question 4

Which of the following is the correct factorization of $$4x^3 - 27$?

Accepted Answer

$$(2x-3)(4x^2+6x+9$$)$$

Question 5

Given $$10(2a-3)^2 - 19(2a-3) - 15$, factor completely.

Accepted Answer

$$2(4a-11)(5a+3)$$

Question 6

Which of the following is the correct factorization of $$6x^2 - 7x - 15$?

Accepted Answer

$$3(x-5)(2x+1)$$

Question 7

If $$x = 2$$, what is the value of $$3x^2 + 6x - 45$?

Accepted Answer

$$-21$$

Question 8

Which of the following is a correct step in factoring $$x^2 + 2x - 15$?

Accepted Answer

Find two numbers that multiply to $$-15$$ and add to $$2$$

Question 9

Which of the following is the result of dividing $$x^2 + 7x + 14$ by x + 2$?

Accepted Answer

$$x + 5$$

Question 10

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

Accepted Answer

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

Question 11

If $$x = -3$$, what is the value of $$x(x^2-49$$)$$?

Accepted Answer

$$-180$$

Question 12

Which of the following is the correct simplification of $$(2x^3)(3x^2$)(4x^2$$)$$?

Accepted Answer

$$24x^7$$

Question 13

Which of the following is the correct factorization of $$x^2 + 2x - 15$?

Accepted Answer

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

Question 14

Which of the following is the correct factorization of $$4x^3 - 27$ using the sum/difference of cubes?

Accepted Answer

$$(2x-3)(4x^2+6x+9$$)$$

Question 15

Which of the following is the correct factorization of $$10(2a-3)^2 - 19(2a-3) - 15$?

Accepted Answer

$$2(4a-11)(5a+3)$$

College Algebra Study Guide: Factoring and Simplifying Expressions

Study Guide - Practice Questions