Answer
$p(x)=2x^2+5x+7$.
Work Step by Step
Write the equation.
$\Rightarrow \frac{p(x)}{x-4}=2x+13+\frac{59}{x-4}$
Multiply the equation by $(x-4)$.
$\Rightarrow (x-4)\left (\frac{p(x)}{x-4} \right )=(x-4) \left ( 2x+13+\frac{59}{x-4} \right )$
Using the distributive property on the right hand side:
$\Rightarrow p(x)=(x-4) (2x+13)+(x-4)\left (\frac{59}{x-4} \right )$
Simplify by using the FOIL method.
$\Rightarrow p(x)=2x^2+13x-8x-52+59$
Add like terms.
$\Rightarrow p(x)=2x^2+5x+7$.
