[tex]p(x)=q(x)(x+2)+r(x)[/tex]
Notice that if [tex]x=-2[/tex], we're left with [tex]p(-2)=r(-2)[/tex].
Synthetic division yields
-2 | 1 2 -8 -18 -9
. | -2 0 16 4
- - - - - - - - - - - - - - - - - - -
. | 1 0 -8 -2 -5
[tex]\implies\dfrac{p(x)}{x+2}=\dfrac{x^4+2x^3-8x^2-18x-9}{x+2}=x^3+4x^2-18-\dfrac5{x+2}[/tex]
[tex]\implies p(x)=(x^3+4x^2-18)(x+2)-5[/tex]
[tex]\implies p(-2)=-5[/tex]
so the answer is (B).
