Question

Divide {eq}(x^3+6x^2-20)

{/eq} by {eq}x^2+2

{/eq}, using long division.

EXPERT ANSWER

Let us divide {eq}x^3 + 6x^2 – 20

{/eq} by {eq}x^2 + 2

{/eq} using the long division:

Here, the divisor is, {eq}d(x)= x^2+2

{/eq},

the dividend is, {eq}p(x)=x^3 + 6x^2 – 20

{/eq},

the quotient is, {eq}q(x)= x+6

{/eq},

and the remainder is, {eq}r(x)=-2x-32

{/eq}.

Using the Euclidean algorithm, the result is:

$$p(x) div d(x) = q(x) + dfrac{r(x)}{d(x)}

$$

We substitute all the values here:

$$left(begin{array}{cc}

x^{3}+6 x^{2} & -20

end{array}right) divleft(x^{2}+2right)= color{blue}{boxed{mathbf{x+6+frac{-2 x-32}{x^{2}+2}}}}

$$