Question

Use synthetic division and the remainder theorem to find p(-2) if p(x)=x^(4)+2x^(3)-8x^(2)-18x-9

A. -6
B. -5
C. -4
D. none of these

Answer 1

`p(x)=q(x)(x+2)+r(x)`

Notice that if
`x=-2`, we're left with
`p(-2)=r(-2)`.

Synthetic division yields

-2 | 1 2 -8 -18 -9
. | -2 0 16 4
- - - - - - - - - - - - - - - - - - -
. | 1 0 -8 -2 -5


`\implies(p(x))/(x+2)=(x^4+2x^3-8x^2-18x-9)/(x+2)=x^3+4x^2-18-\frac5{x+2}`

`\implies p(x)=(x^3+4x^2-18)(x+2)-5`

`\implies p(-2)=-5`

so the answer is (B).