Steps to Factoring

These guidelines are for an Intermediate Algebra Level of understanding.

Greatest Common Factor

Always begin by factoring out the greatest common factor (GCF) if it is anything other than 1.

\( 15x^3-35x^2-30x \Longrightarrow 5x ( 3x^3-7x-6 ) \)

Look at the number of terms

If there are two terms

The difference of two squares and difference of two cubes are special cases of the broader difference of two nth-degree terms.

If there are three terms

If there are four or more terms

Check for futher factorability

After you have factored, check what remains to see if it can be factored more.

For example, if you choose to factor \( x^4 - y^4 \) as the difference of two squares, you get: \( x^4 - y^4 = (x^2 - y^2)(x^2 + y^2) \), but the \(x^2 - y^2\) can be factored further as \( (x-y)(x+y) \). So we get \( x^4 - y^4 = (x^2 - y^2)(x^2 + y^2) = (x-y)(x+y)(x^2+y^2) \)