# How do you factor and find the zeroes for P(x)= x^2 - 9?

Jun 2, 2015

The zeros of a function $P \left(x\right)$ are the values of $x$ for which $P \left(x\right) = 0$

By the difference of squares:

$\textcolor{w h i t e}{\text{XXXXX}}$${x}^{2} - 9 = \left(x + 3\right) \left(x - 3\right)$

If $P \left(x\right) = 0$ then

$\textcolor{w h i t e}{\text{XXXXX}}$$\left(x + 3\right) \left(x - 3\right) = 0$

which can only be true if

either

$\textcolor{w h i t e}{\text{XXXXX}}$$x = - 3$ or $x = + 3$