# 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.

## Glossary

**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

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