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