GCF and Group Factoring

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the given numbers 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

What is the first step in factoring a polynomial?

Back

The first step is to identify and factor out the GCF from all the terms in the polynomial.

Front

Factor the expression: 7r^3 - 8r^2 + 42r - 48

Back

(r^2 + 6)(7r - 8)

Front

Factor the expression: 2x^3 - 8x^2 - x + 4

Back

(2x^2 - 1)(x - 4)

Front

What does it mean to factor out the GCF?

Back

Factoring out the GCF means to divide each term of the polynomial by the GCF and express the polynomial as a product of the GCF and the remaining polynomial.

Front

Factor the expression: 18x^3 + 81x - 27

Back

9(2x^3 + 9x - 3)

Front

Factor the expression: 16xy - 24y

Back

8y(2x - 3)

Front

Factor the expression: 3x^3 + 9x

Back

3x(x^2 + 3)

Front

What is a polynomial?

Back

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