# How do you evaluate the function p(x)=1/2x^3 + 2/3x^2 - 1/4x + 1/3 for p(-2)?

Mar 24, 2018

$p \left(- 2\right) = \frac{1}{2} {\left(- 2\right)}^{3} + \frac{2}{3} {\left(- 2\right)}^{2} - \frac{1}{4} \left(- 2\right) + \frac{1}{3}$
$= \frac{1}{2} \left(- 8\right) + \frac{2}{3} \left(4\right) + \frac{2}{4} + \frac{1}{3}$
$= - \frac{8}{2} + \frac{8}{3} + \frac{2}{4} + \frac{1}{3}$
$= - 4 + \left(\frac{8}{3} + \frac{1}{3}\right) + \frac{1}{2}$
$= - 4 + \frac{9}{3} + \frac{1}{2}$
$= - 4 + 3 + \frac{1}{2}$
$= - 1 + \frac{1}{2}$
$= - \frac{2}{2} + \frac{1}{2}$
$= \frac{- 2 + 1}{2}$
$= - \frac{1}{2}$

#### Explanation:

Just put the $x = - 2$ on the polynomial equation and you will simplify and you will get $p \left(- 2\right) = - \frac{1}{2}$