Answer
$f(-2)=75$
Work Step by Step
We are given the polynomial
$$f(x)=8x^4+12x^3+6x^2-5x+9.$$
The polynomial value for $x=-2$ is the remainder of the division of $f$ by $x-(-2)=x+2$.
We use synthetic division.
First we write the coefficients of $f$ in order of descending coefficients and write the value at which $f$ is being evaluated to the left.
Then we bring down the leading coefficient, multiply the leading coefficient by the $x$-value, write the product under the second coefficient, and add.
Then we multiply the previous sum by the $x$-value, write the product under the third coefficient, and add. Perform this for all the remaining coefficients. We get the value of $f$ at the given $x$-value as the final sum.
$$f(-2)=75.$$
