Question 1

Which of the following best defines the Greatest Common Factor (GCF) of a set of integers?

Accepted Answer

The largest integer that is a factor of all the integers in the list.

Question 2

What is the GCF of $$30$$, $$75$$, and $$135$$?

Accepted Answer

$$15$$

Question 3

Find the GCF of $$p^2q$, p^3$q^2$$, and $$pq^3$.

Accepted Answer

$$pq$$

Question 4

What is the GCF of $$-21x^3$$ and $$14x$$?

Accepted Answer

$$7x$$

Question 5

Which of the following is the GCF of $$15y^3$$, $$5y^5$$, and $$-20y^2$$?

Accepted Answer

$$5y^2$$

Question 6

When factoring $$4x^3$$ + $$12x^2 - 8x$, what is the first step?

Accepted Answer

Find the GCF of the coefficients and variables.

Question 7

Factor $$4x^3$$ + $$12x^2 - 8x$ completely.

Accepted Answer

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

Question 8

What is the result of factoring $$4b^3$$ - $$2b^2 - 6b$ by its GCF?

Accepted Answer

$$2b(2b^2 - b - 3$$)$$

Question 9

A chemist is mixing three solutions with concentrations represented by $$12y^4$$, $$4y^3$$, and $$-6y^2. $$What is the GCF of these concentrations?

Accepted Answer

$$2y^2$$

Question 10

Factor $$12y^4$$ + $$4y^3$$ - $$6y^2$$ completely.

Accepted Answer

$$2y^2(6y^2$ + 2y - 3)$

Question 11

A medical researcher is analyzing data represented by $$3n^3$$ + $$15n^2 + 18n$. What is the GCF of these terms?

Accepted Answer

$$3n$$

Question 12

Factor $$3n^3$$ + $$15n^2 + 18n$ completely.

Accepted Answer

$$3n(n^2 + 5n + 6$$)$$

Question 13

Which of the following steps is NOT part of the process for factoring out the GCF?

Accepted Answer

Multiply each term by the GCF.

Question 14

If you factor $$-21x^3 + 14x$ by its GCF, what is the resulting expression?

Accepted Answer

$$7x(-3x^2 + 2$$)$$

Question 15

A factory produces three types of widgets: $$15y^3$$, $$5y^5$$, and $$-20y^2$$ units. What is the GCF for the production numbers?

Accepted Answer

$$5y^2$$

Question 16

After factoring $$15y^3$$ + $$5y^5$$ - $$20y^2 by $$its GCF, what is the resulting expression?

Accepted Answer

Question 17

Which of the following is the correct GCF for the terms $$4x^3$$, $$12x^2$$, and $$-8x$$?

Accepted Answer

$$4x$$

Question 18

If you factor $$4x^3$$ + $$12x^2 - 8x$ and then set the resulting expression equal to zero, which equation would you solve?

Accepted Answer

$$4x(x^2 + 3x - 2) = 0$

Question 19

Which of the following best describes the GCF of common variables in a list of terms?

Accepted Answer

The variable raised to the lowest power present in all terms.

Factoring and the Greatest Common Factor (GCF)

Study Guide - Practice Questions