Question

Use synthetic division to find P (-10) for P(x)=2x^3+14x^2-58x

Answer 1

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 $p(-10)=2$.