# How do you determine p(c) given p(x)=4x^2-33x-180 and c=12?

Aug 31, 2016

$p \left(12\right) = 0$

#### Explanation:

To determine p(c), substitute x = c into p(x).

$\Rightarrow p \left(\textcolor{red}{c}\right) = 4 {\left(\textcolor{red}{c}\right)}^{2} - 33 \left(\textcolor{red}{c}\right) - 180$

Thus $p \left(c\right) = 4 {c}^{2} - 33 c - 180$

Similarly to evaluate p(c) when c = 12, substitute c = 12 into p(c)

$\Rightarrow p \left(\textcolor{red}{12}\right) = 4 {\left(\textcolor{red}{12}\right)}^{2} - 33 \left(\textcolor{red}{12}\right) - 180$

Hence $p \left(12\right) = \left(4 \times 144\right) - \left(33 \times 12\right) - 180 = 0$