# How do you find the zeros of y = (x + 2)(x − 4)(x + 1)?

Jun 24, 2016

$x = - 2$, $x = 4$ and $x = - 1$

#### Explanation:

A product of three numbers is zero if and only if at least one of the numbers is zero.

In our example:

$y = \left(x + 2\right) \left(x - 4\right) \left(x + 1\right)$

So $\left(x + 2\right) \left(x - 4\right) \left(x + 1\right) = 0$ if and only if at least one of the following holds:

• $\left(x + 2\right) = 0 \textcolor{w h i t e}{X X}$ i.e. $x = - 2$
• $\left(x - 4\right) = 0 \textcolor{w h i t e}{X X}$ i.e. $x = 4$
• $\left(x + 1\right) = 0 \textcolor{w h i t e}{X X}$ i.e. $x = - 1$

So the three zeros are: $x = - 2$, $x = 4$ and $x = - 1$