Summary: Factoring Polynomials

Key Equations

difference of squares [latex]{a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)[/latex]
perfect square trinomial [latex]{a}^{2}+2ab+{b}^{2}={\left(a+b\right)}^{2}[/latex]
sum of cubes [latex]{a}^{3}+{b}^{3}=\left(a+b\right)\left({a}^{2}-ab+{b}^{2}\right)[/latex]
difference of cubes [latex]{a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)[/latex]

Key Concepts

  • The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem.
  • Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term.
  • Trinomials can be factored using a process called factoring by grouping.
  • Perfect square trinomials and the difference of squares are special products and can be factored using equations.
  • The sum of cubes and the difference of cubes can be factored using equations.
  • Polynomials containing fractional and negative exponents can be factored by pulling out a GCF.


factor by grouping
a method for factoring a trinomial of the form [latex]a{x}^{2}+bx+c[/latex] by dividing the x term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression
greatest common factor
the largest polynomial that divides evenly into each polynomial