Answer
For the long division problem $5x-2\overset{2{{x}^{2}}}{\overline{\left){10{{x}^{3}}+6{{x}^{2}}-9x+10}\right.}}$ , the next step is to multiply $2{{x}^{2}}$ and $5x-2$. Obtain $10{{x}^{3}}-4{{x}^{2}}$. Write this result below $10{{x}^{3}}+6{{x}^{2}}$.
Work Step by Step
Let us consider,
$5x-2\overset{2{{x}^{2}}}{\overline{\left){10{{x}^{3}}+6{{x}^{2}}-9x+10}\right.}}$.
Dividend:
$10{{x}^{3}}+6{{x}^{2}}-9x+10$.
Divisor:
$5x-2$.
We divide:
$5x-2\overset{2{{x}^{2}}+2x-1}{\overline{\left){\begin{align}
& 10{{x}^{3}}+6{{x}^{2}}-9x+10 \\
& \underline{10{{x}^{3}}-4{{x}^{2}}} \\
& \text{ }10{{x}^{2}}-9x \\
& \text{ }\underline{10{{x}^{2}}-4x} \\
& \text{ }-5x+10 \\
& \text{ }\underline{-5x+2} \\
& \text{ }8 \\
\end{align}}\right.}}$
Thus, the next step is to multiply $2{{x}^{2}}$ and $5x-2$ to obtain $10{{x}^{3}}-4{{x}^{2}}$. Write this result below $10{{x}^{3}}+6{{x}^{2}}$.
