Factoring Trinomials with GCF

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers have in common.

Front

How do you factor a trinomial?

Back

To factor a trinomial, look for two numbers that multiply to the constant term and add to the coefficient of the middle term.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, including the GCF.

Front

What is the first step in factoring a trinomial with GCF?

Back

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

Front

Factor the trinomial: 2x^2 + 4x + 2

Back

2(x^2 + 2x + 1) = 2(x + 1)^2

Front

Factor the trinomial: x^2 + 5x + 6

Back

(x + 2)(x + 3)

Front

What is the role of the GCF in factoring?

Back

The GCF simplifies the expression and makes it easier to factor the remaining polynomial.

Front

Factor the trinomial: 3x^2 + 12x + 12

Back

3(x^2 + 4x + 4) = 3(x + 2)^2

Front

What is the difference between factoring and expanding?

Back

Factoring breaks down an expression into simpler components, while expanding multiplies out the components.