Factoring out a GCF

Front

What does GCF stand for in mathematics?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

Front

How do you find the GCF of two numbers?

Back

To find the GCF of two numbers, list the factors of each number and identify the largest factor that appears in both lists.

Front

What is the first step in factoring out the GCF from an expression?

Back

The first step is to identify the GCF of all the terms in the expression.

Front

Factor the expression: 12x + 8.

Back

4(3x + 2).

Front

What is the GCF of the coefficients 45, 15, and 10?

Back

The GCF of 45, 15, and 10 is 5.

Front

How do you factor the expression 2x^3 + 2x^2 - 6x?

Back

First, identify the GCF, which is 2x, then factor it out to get 2x(x^2 + x - 3).

Front

What is the result of factoring out the GCF from the expression 6x + 3y?

Back

Factoring out the GCF gives 3(2x + y).

Front

What is the GCF of the terms 10r^3s^2, 25r^2s^2, and -15r^2s^3?

Back

The GCF is 5r^2s^2.

Front

How do you factor the expression 2n^2 - 8n^3?

Back

Factor out the GCF, which is 2n^2, to get 2n^2(1 - 4n^2).

Front

What is the importance of factoring out the GCF in polynomial expressions?

Back

Factoring out the GCF simplifies the expression and makes it easier to solve or further factor.