Question 1

Factor completely: $$3x^2 + 6x - 45$

Accepted Answer

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

Question 2

Factor completely: $$x^3 - 49x$

Accepted Answer

$$x(x^2$$ - $$7)(x^2 + 7$$)$$

Question 3

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

Accepted Answer

$$24x^9$$

Question 4

Factor completely: $$4x^3 - 27$

Accepted Answer

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

Question 5

Factor completely: $$10(2a - 3)^2$ - 19(2a - 3) - 15$$

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

Given $$x^2 + 2x - 15$, which of the following is its factorization?

Accepted Answer

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

Question 8

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

Accepted Answer

$$-21$$

Question 9

Which of the following expressions is equivalent to $$x^3 - 49x$?

Accepted Answer

$$x(x^2 - 49$$)$$

Question 10

Which of the following is the result of multiplying $$(2x^3)(3x^2$)$?

Accepted Answer

$$6x^5$$

Question 11

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

Accepted Answer

$$-8 - 98 = -106$$

Question 12

Which of the following is a factor of $$4x^3 - 27$?

Accepted Answer

$$2x - 3$$

Question 13

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

Accepted Answer

$$24x^9$$

Question 14

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

Accepted Answer

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

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: Factoring and Simplifying Expressions Study Guide

Study Guide - Practice Questions