# p(x)=3x^2-x^2+2x-5, what is p(x) when x=-2 and x=3?

Mar 29, 2017

$p \left(- 2\right) = - 37 \text{ and } p \left(3\right) = 73$

#### Explanation:

To evaluate p( -2 ) and p( 3 ) substitute x = - 2 and x = 3
into p( x )

$\Rightarrow p \left(\textcolor{red}{- 2}\right) = 3 {\left(\textcolor{red}{- 2}\right)}^{3} - {\left(\textcolor{red}{- 2}\right)}^{2} + 2 \left(\textcolor{red}{- 2}\right) - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(- 2\right)} = \left(3 \times - 8\right) - \left(+ 4\right) + \left(2 \times - 2\right) - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(- 2\right)} = - 24 - 4 - 4 - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(- 2\right)} = - 37$

$\Rightarrow p \left(\textcolor{m a \ge n t a}{3}\right) = 3 {\left(\textcolor{m a \ge n t a}{3}\right)}^{3} - {\left(\textcolor{m a \ge n t a}{3}\right)}^{2} + 2 \left(\textcolor{m a \ge n t a}{3}\right) - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(3\right)} = \left(3 \times 27\right) - 9 + 6 - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(3\right)} = 81 - 9 + 6 - 5$

$\textcolor{w h i t e}{\Rightarrow p \left(3\right)} = 73$

Mar 29, 2017

$p \left(- 2\right) = - 37 \mathmr{and} p \left(3\right) = 73$

#### Explanation:

This is an function, which means that all values of $x$ would satisfy the equation.

When $x = - 2$,

$p \left(- 2\right) = 3 {\left(- 2\right)}^{3} - {\left(- 2\right)}^{2} + 2 \left(- 2\right) - 5$
$\textcolor{w h i t e}{\times x / .} = - 24 - 4 - 4 - 5$
$\textcolor{w h i t e}{\times x / .} = - 37$

When $x = 3$,

$p \left(3\right) = 3 {\left(3\right)}^{3} - {\left(3\right)}^{2} + 2 \left(3\right) - 5$
$\textcolor{w h i t e}{x / .} = 81 - 9 + 6 - 5$
$\textcolor{w h i t e}{x / .} = 73$