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

The polynomial remainder theorem states that the remainder upon dividing a polynomial by is the same as the value of , so to find you need to find the remainder upon dividing



You have

..... | 2 ...  14  ... -58
-10 |    ... -20  ... 60
--------------------------
..... | 2 ...  -6  ....  2

So the quotient and remainder upon dividing is



with a remainder of 2, which means .