Question

Use synthetic division and the Remainder Theorem to find the indicated function value. Show all work.

Answer 1

To determine the given function using a remainder theorem :

`f(x)=x^4+5x^3+5x^2-5x-6`

The given function can be solved by substituting x = 3

`\begin{gathered} f(x)=x^4+5x^3+5x^2-5x-6 \\ f(3)=3^4+5(3)^3+5(3)^2-5(3)-6 \\ f(3)=81+135+45-15-6 \end{gathered}`

Adding up the values

`\begin{gathered} f(3)=81+135+45-15-6 \\ f(3)=240 \end{gathered}`

Hence the final value of f(3) = 240