Educator

Factoring Using Greatest Common Factor

• You can use the distributive property to factor the greatest common factor out of each polynomial in a sum or difference of polynomials.

• For a polynomial with 4 terms, factor a GCF out of the first two terms and then factor the GCF out of the second two terms. Then factor the common binomial factor. This is called factoring by grouping.

• Sometimes in factoring by grouping, you must use the fact that one binomial factor is the additive inverse of another one. Factoring –1 out of one of these binomials produces two identical binomial factors and enables you to complete the factoring by grouping.

• The Zero Product Property states that if a product of two factors is 0, then one or both of the factors must be equal to 0. This property allows you to solve equations in which a factored polynomial is equal to 0.

• The solutions of an equation are also called the roots of the equation.