anonymous
  • anonymous
what is the remainder of the division problem shown below (x^3+2x^2-6x-9)/(x+2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
would you agree that: \[\frac{p(x)}{x-a}=q(x)+\frac{r(x)}{x-a}\]
amistre64
  • amistre64
for example \[\frac 54=1+\frac14\]
anonymous
  • anonymous
yes

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amistre64
  • amistre64
then lets simplify it, by multiply both sides by x-a \[p(x)=(x-a)~q(x)+r(x)\] do we still agree?
anonymous
  • anonymous
yes we do
amistre64
  • amistre64
now, let x=a \[p(a)=\underbrace{(a-a)}_{\color{red}{=0}}~q(a)+r(a)\] \[p(a)=r(a)\]
amistre64
  • amistre64
now, how can we apply this to your question
amistre64
  • 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?
anonymous
  • anonymous
ok thanks i got it from here
amistre64
  • amistre64
good luck :)

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