# 4.9 Review and Summary

Access these online video resources for additional instruction and practice with factoring polynomials.

## Key Equations

Perfect square trinomial $\left(x+a\right)^2=\left(x+a\right)\left(x+a\right)=x^2+2ax+a^2$ $a^2+2ab+b^2=\left(a+b\right)^2$ $\left(a+b\right)\left(a-b\right)=a^2-b^2$ $a^2-b^2=\left(a+b\right)\left(a-b\right)$ $a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$ $a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$

## Key Terms

Binomial – a polynomial containing two terms

Coefficient – any real number $a_i$ in a polynomial in the form $a_nx^n+...+a_2x^2+a_1x+a_0$

Difference of Squares – the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign

Distributive Property – the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, $a⋅(b+c)=a⋅b+a⋅c$

Factor by Grouping – a method for factoring a trinomial in the form $ax^2+bx+c$ 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

Leading Term – the term containing the highest degree

Perfect Square Trinomial – the trinomial that results when a binomial is squared

Trinomial – a polynomial containing three terms