a4kat
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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

Respuesta :

LammettHash
[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).

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