Factoring GCF

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the coefficients of a polynomial without leaving a remainder.

Front

How do you find the GCF of two numbers?

Back

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

Front

Factor the expression: 10a^4 + 16a + 10a^2

Back

2a(5a^3 + 8 + 5a)

Front

What is the first step in factoring a polynomial?

Back

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

Front

Factor the expression: 4b^5 + 4b^3 + 16b^2

Back

4b^2(b^3 + b + 4)

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest factors, including all GCFs.

Front

Factor the expression: 16xy - 24y

Back

8y(2x - 3)

Front

What is the role of coefficients in factoring?

Back

Coefficients are the numerical factors in a polynomial that can be included in the GCF.

Front

Factor the expression: 80x^5 - 70x^2 - 60x^7

Back

10x^2(8x^3 - 7 - 6x^5)

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication.