Factoring Out Greatest Common Factor (GCF) in Algebra

Questions and Answers

To simplify the quadratic expression and make it easier to work with (correct)

To find the vertex of the quadratic function

To determine the axis of symmetry of the quadratic function

To find the solutions to the quadratic equation

Divide each term by the GCF

Rewrite the expression as a product of the GCF and the remaining factors

Solve the quadratic equation

Identify the GCF of all terms in the expression (correct)

2x^2 + 6x + 1

x^2 + 3x + 2

2(x^2 + 3x + 2) (correct)

x^2 + 6x + 4

The largest common factor that divides all terms of the expression Signup and view all the answers

Because it simplifies the quadratic expression and makes it easier to work with Signup and view all the answers

Each term is divided by the GCF Signup and view all the answers

Study Notes

What is Factoring Out GCF?

Factoring out the Greatest Common Factor (GCF) is a method used to simplify quadratic expressions.
It involves finding the common factor that divides all terms of the expression and rewriting the expression as a product of the GCF and the remaining factors.

How to Factor Out GCF

Find the GCF: Identify the greatest common factor of all terms in the quadratic expression.
Rewrite the expression: Divide each term by the GCF and rewrite the expression as a product of the GCF and the remaining factors.

Example

Key Points

Factoring out the GCF simplifies the quadratic expression and makes it easier to work with.
The GCF is the largest common factor that divides all terms of the expression.
Factoring out the GCF is a crucial step in solving quadratic equations and graphing quadratic functions.

Factoring out the Greatest Common Factor (GCF) is a method used to simplify quadratic expressions by finding the common factor that divides all terms of the expression and rewriting it as a product of the GCF and the remaining factors.

Find the GCF of all terms in the quadratic expression.
Divide each term by the GCF and rewrite the expression as a product of the GCF and the remaining factors.

Factoring out the GCF simplifies the quadratic expression and makes it easier to work with.
The GCF is the largest common factor that divides all terms of the expression.
Factoring out the GCF is a crucial step in solving quadratic equations and graphing quadratic functions.