Key Terms

difference of squares pattern

If a and b are real numbers,

factoring

Factoring is splitting a product into factors; in other words, it is the reverse process of multiplying.

greatest common factor

The greatest common factor is the largest expression that is a factor of two or more expressions is the greatest common factor (GCF).

perfect square trinomials pattern

If a and b are real numbers,

$$\begin{array}{cccc}\hfill a^2+2ab+b^2={\left(a+b\right)}^2\hfill & & & \hfill a^2-2ab+b^2={\left(a-b\right)}^2\hfill \end{array}$$

prime polynomials

Polynomials that cannot be factored are prime polynomials.

quadratic equations

are equations in which the variable is squared.

sum and difference of cubes pattern

$$\begin{array}{c}\hfill a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)\hfill \\ \hfill a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\hfill \end{array}$$

Zero Product Property

The Zero Product Property states that, if the product of two quantities is zero, at least one of the quantities is zero.