Question

(An Intermediate Algebra review exercise) Use polynomial long division to perform the indicated division. Write the polynomial in the form
p(x) = d(x)q(x) + r(x).
(8x^4−3x^3+2x^2−8)÷(x^2+4)

Answer 1

I got the answer (-3x+10)+(12x-48/x^2+4) But I am not sure how to put it in the p(x)=d(x)q(x)+r(x) form.

Answer 2

Dividend = Quotient * Divisor + Remainder

(8x^4 − 3x^3 +2x^2 − 8) =

(8x^2 -3x -30) * (x^2 + 4) + 12x + 112

@johnkuang123

Answer 3

***I got the answer (-3x+10)+(12x-48/x^2+4) ***

with p= (8x^4−3x^3+2x^2−8)
and d= (x^2+4)
then
\[ \frac{p}{d} = q + \frac{r}{d} \]
i.e. you get a quotient q and a remainder polynomial r that is divided by d
if you multiply both sides by d you get
\[ \frac{p}{\cancel{d}}\cdot \cancel{d}= q\cdot d + \frac{r}{\cancel{d}}\cdot \cancel{d}\\
p= q \cdot d + r
\]

in other words, once you find the quotient q and at the remainder r
you can write
p= q * d + r

Answer 4

However, your result is not correct
the work should look like this: