The polynomial remainder theorem states that the remainder upon dividing a polynomial \(p(x)\) by \(x-c\) is the same as the value of \(p(c)\), so to find \(p(-10)\) you need to find the remainder upon dividing
\(\dfrac{2x^3+14x^2-58x}{x+10}\)
You have
..... | 2 ... 14 ... -58
-10 | ... -20 ... 60
--------------------------
..... | 2 ... -6 .... 2
So the quotient and remainder upon dividing is
\(\dfrac{2x^3+14x^2-58x}{x+10}=2x-6+\dfrac2{x+10}\)
with a remainder of 2, which means \(p(-10)=2\).
