Question

Divide -2x^3+21x^2-20x-12 by (x-3)

Answer 1

Use synthetic division:
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/synthetic-division/v/synthetic-division

Answer 2

\[p(x) = -2x^{3}+21x^{2}-20x-12\]
\[q(x) = x-3\]
Use the synthetic division table:
\[\begin{matrix}\begin{array}{r} 3 \\ ~ \end{array} &
\underline
{
\begin{array}{rrrr}
-2&21&-20&-12\\
~~~~&-6&45&75
\end{array}
}
\\
~
&
\begin{array}{rrrr}
\color{blue}{ -2 }&\color{blue}{ 15 }&\color{blue}{ 25 }&\color{red}{ 63 }
\end{array}\end{matrix}\]
\[\frac{ -2x^{3}+21x^{2}-20x-12 }{ x-3 } = \color{blue}{ -2 }x^{2}~\color{blue}{ + }~\color{blue}{ 15 }x~\color{blue}{ + }~\color{blue}{ 25 } ~+~ \frac{ \color{red}{ 63 } }{ x-3 }\]

Answer 3

Okay, thanks.

Answer 4

Do you understand?

Answer 5

Somewhat, yeah.

Answer 6

Is there anything I can do to help clarify?

Answer 7

I'm not really able to do normal division, even. This is about as good as I'm going to get on it.

Answer 8

Thank you though.

Answer 9

The Khan Academy video explain really well on what I did, I highly recommend you watch it.

Answer 10

I will, thanks!

Answer 11

Good luck!