determine the remainder when (2x^4-12x^3-13x^2+4x-9) is divided by (x+7)

Question

answer options are

a) 37

b) 12

c) 0

d) -9

Answer 1

Multiply each by x, then do each by 7. Add the like-terms.

Answer 2

if x+7 is a factor then x=-7 is a solution...

(2x^4-12x^3-13x^2+4x-9) when x=-7

2(-7)^4 - 12(-7)^3 - 13(-7)^2 + 4(-7) - 9 =

2*(2401) - 12( -343) - 13(49) + (-28) - 9 =

4802 +4116 - 637 - 28 - 9=8244

Here's the long division to back it up

-7 | 2 -12 -13 4 -9

-14 182 -1183 8253

____________________________

2 -26 169 -1179 8244