Summary: Factoring Polynomials
- Find the greatest common factor.
- Factor each coefficient into primes. Write all variables with exponents in expanded form.
- List all factors—matching common factors in a column. In each column, circle the common factors.
- Bring down the common factors that all expressions share.
- Multiply the factors.
- Distributive Property
- If [latex]a[/latex] , [latex]b[/latex] , [latex]c[/latex] are real numbers, then[latex]a\left(b+c\right)=ab+ac[/latex] and [latex]ab+ac=a\left(b+c\right)[/latex]
- Factor the greatest common factor from a polynomial.
- Find the GCF of all the terms of the polynomial.
- Rewrite each term as a product using the GCF.
- Use the Distributive Property ‘in reverse’ to factor the expression.
- Check by multiplying the factors.
- greatest common factor
- The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.