# How do you determine p(c) given p(x)=3x^3-6x^2+4x-8 and c=2?

Sep 17, 2016

0

#### Explanation:

Express p(x) as p(c) by substituting x = c in for x in p(x).

$p \left(\textcolor{b l u e}{c}\right) = 3 {\left(\textcolor{b l u e}{c}\right)}^{3} - 6 {\left(\textcolor{b l u e}{c}\right)}^{2} + 4 \left(\textcolor{b l u e}{c}\right) - 8$

$\Rightarrow p \left(c\right) = 3 {c}^{3} - 6 {c}^{2} + 4 c - 8$

To evaluate p(2) substitute c=2 in for c in p(c)

$\Rightarrow p \left(\textcolor{red}{2}\right) = 3 {\left(\textcolor{red}{2}\right)}^{3} - 6 {\left(\textcolor{red}{2}\right)}^{2} + 4 \left(\textcolor{red}{2}\right) - 8$

$= 24 - 24 + 8 - 8 = 0$