Question

Divide (12x⁴- 6x³- 8x²+4x) by 2x​

Answer 1

Answer:

x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)

(x3 + 3x2 + 5x – 4) – 1(3x3 – 8x2 – 5x + 6)

(x3 + 3x2 + 5x – 4) – 1(3x3) – 1 (–8x2) – 1(–5x) – 1(6)

x3 + 3x2 + 5x – 4 – 3x3 + 8x2 + 5x – 6

x3 – 3x3 + 3x2 + 8x2 + 5x + 5x – 4 – 6

–2x3 + 11x2 + 10x –10

And here's what the subtraction looks like, when going vertically:

\small{ \begin{array}{rrrr}x^3&+3x^2&+5x&-4\\-(3x^3&-8x^2&-5x&+6)\\ \hline\end{array} }

x

3

−(3x

3

+3x

2

−8x

2

+5x

−5x

−4

+6)

I'll change all the signs in the second row (shown in red below), and add down:

\small{ \begin{array}{rrrr}x^3&+3x^2&+5x&-4\\ \textcolor{red}{\textbf{--}}\,3x^3&\textcolor{red}{\textbf{+}}\,8x^2&\textcolor{red}{\textbf{+}}\,5x&\textcolor{red}{\textbf{--}}\,6\\ \hline -2x^3&+11x^2&+10x&-10\end{array} }

x

3

–3x

3

−2x

3

+3x

2

+8x

2

+11x

2

+5x

+5x

+10x

−4

–6

−10

Either way, I get the answer:

–2x3 + 11x2 + 10x – 10