Given,

\(\displaystyle\frac{{{x}^{{3}}+{5}{x}^{{2}}-{7}{x}−{4}}}{{{x}−{2}}}\)

On dividing, we get

\(\displaystyle{\left({x}-{2}\right)}{x}^{{3}}+{5}{x}^{{2}}-{7}{x}-{4}{\left({x}^{{2}}+{7}{x}+{7}\right)}\)

\(\displaystyle\frac{{{x}^{{3}}-{2}{x}^{{2}}}}{{{7}{x}^{{2}}-{7}{x}}}\)

\(\displaystyle\frac{{{7}{x}^{{2}}-{14}{x}}}{{{7}{x}-{4}}}\)

\(\displaystyle\frac{{{7}{x}-{4}}}{{{10}}}\)

Step 2

Therefore,

Quotient is \(\displaystyle{x}^{{2}}+{7}{x}+{7}\) & reminder is 10.

\(\displaystyle\frac{{{x}^{{3}}+{5}{x}^{{2}}-{7}{x}−{4}}}{{{x}−{2}}}\)

On dividing, we get

\(\displaystyle{\left({x}-{2}\right)}{x}^{{3}}+{5}{x}^{{2}}-{7}{x}-{4}{\left({x}^{{2}}+{7}{x}+{7}\right)}\)

\(\displaystyle\frac{{{x}^{{3}}-{2}{x}^{{2}}}}{{{7}{x}^{{2}}-{7}{x}}}\)

\(\displaystyle\frac{{{7}{x}^{{2}}-{14}{x}}}{{{7}{x}-{4}}}\)

\(\displaystyle\frac{{{7}{x}-{4}}}{{{10}}}\)

Step 2

Therefore,

Quotient is \(\displaystyle{x}^{{2}}+{7}{x}+{7}\) & reminder is 10.