Answer
$4x^2-x+10-\frac{6}{x+7}$
Work Step by Step
We have to perform the division
$$\dfrac{f(x)}{x-a}=\dfrac{4x^3+27x^2+3x+64}{x+7}.$$
We use synthetic division.
First we write the coefficients of $f$ in order of descending coefficients and write the value of $a$ 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. The final sum is the remainder. Therefore we got:
$$\dfrac{4x^3+27x^2+3x+64}{x+7}=4x^2-x+10-\dfrac{6}{x+7}.$$
