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
