Divide (12x⁴- 6x³- 8x²+4x) by 2x
Answers
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