Question

Please guide me in the correct direction with attached pic. For p(x)=7+10x-12x^2-10x^3+2x^4+3x^5, evaluate the following;

Answer 1

Solution:

Given:

$p(x)=7+10x-12x^2-10x^3+2x^4+3x^5$

To find p(-3), substitute x = -3

$\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(-3)=7+10\left(-3\right)-12\left(-3\right)^2-10\left(-3\right)^3+2\left(-3\right)^4+3\left(-3\right)^5 \\ p(-3)=-428 \end{gathered}$

To find p(1), substitute x = 1

$\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(1)=7+10\cdot\:1-12\cdot\:1^2-10\cdot\:1^3+2\cdot\:1^4+3\cdot\:1^5 \\ p(1)=0 \end{gathered}$

To find p(5), substitute x = 5

$\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(5)=7+10\cdot\:5-12\cdot\:5^2-10\cdot\:5^3+2\cdot\:5^4+3\cdot\:5^5 \\ p(5)=9132 \end{gathered}$

Therefore, OPTION B is correct.