Question

what is the remainder of the division problem shown below (x^3+2x^2-6x-9)/(x+2)

Answer 1

would you agree that:
\[\frac{p(x)}{x-a}=q(x)+\frac{r(x)}{x-a}\]

Answer 2

for example
\[\frac 54=1+\frac14\]

Answer 3

yes

Answer 4

then lets simplify it, by multiply both sides by x-a
\[p(x)=(x-a)~q(x)+r(x)\]
do we still agree?

Answer 5

yes we do

Answer 6

now, let x=a

\[p(a)=\underbrace{(a-a)}_{\color{red}{=0}}~q(a)+r(a)\]
\[p(a)=r(a)\]

Answer 7

now, how can we apply this to your question

Answer 8

(x^3+2x^2-6x-9) / (x+2) = q(x) + r(x)/(x+2)

x^3+2x^2-6x-9 = (x+2) q(x) + r(x)

when does x+2 = 0?

Answer 9

ok thanks i got it from here

Answer 10

good luck :)