Question

Determine if x-5 is a factor of -2x^3+14x^2+24x+20, how do you know? a. no, because the remainder is -460 b. no, because the remainder is 0 c. yes, because the remainder is -460 d. yes, because the remainder is 0.

Answer 1

d. yes, because the remainder is 0

Explanation:

Answer 2

Let
`f(x)=-2x^3+14x^2+24x+20`. You have
`f(5)=240`, which means - by the polynomial remainder theorem - that the remainder upon dividing
`f(x)` by
`x-5` is 240, and so
`x-5` is not a factor of
`f(x)`.