# How do you factor binomials?

#### Understand the Problem

The question is asking for the process or method used to factor binomials in algebra. This involves identifying common factors or applying formulas to simplify the expression.

Identify the GCF, rewrite, factor out the GCF, and apply special formulas if applicable.

You factor binomials by identifying the greatest common factor, rewriting the binomial using the GCF, factoring out the GCF, and applying special binomial formulas if applicable.

#### Steps to Solve

1. Identify the greatest common factor (GCF)

Identify the largest factor that divides both terms in the binomial.

Example: For the binomial $6x^2 - 9x$, the GCF is $3x$.

1. Rewrite the binomial using the GCF

Express each term as a product of the GCF and another term.

$$6x^2 - 9x = 3x(2x) - 3x(3)$$

1. Factor out the GCF

Remove the GCF from each term, and write it outside the parentheses.

$$6x^2 - 9x = 3x(2x - 3)$$

1. Use special binomial formulas if applicable

For some binomials, special factorization formulas might apply, such as the difference of squares or perfect square trinomials.

• Difference of squares: $a^2 - b^2 = (a - b)(a + b)$
• Perfect square trinomials: $(a - b)^2 = a^2 - 2ab + b^2$
1. Apply the relevant formula to factorize

Check if the binomial fits any of the special formulas, and apply the relevant factorizations.

Example: For $x^2 - 9$, apply the difference of squares formula:

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

You factor binomials by identifying the greatest common factor, rewriting the binomial using the GCF, factoring out the GCF, and applying special binomial formulas if applicable.