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

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1. amistre64

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

2. amistre64

for example $\frac 54=1+\frac14$

3. anonymous

yes

4. amistre64

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

5. anonymous

yes we do

6. amistre64

now, let x=a $p(a)=\underbrace{(a-a)}_{\color{red}{=0}}~q(a)+r(a)$ $p(a)=r(a)$

7. amistre64

now, how can we apply this to your question

8. amistre64

(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?

9. anonymous

ok thanks i got it from here

10. amistre64

good luck :)