Consider the polynomial Division (x^3+5x^2-7x−4)/(x−2)

Question
Polynomial factorization
asked 2021-02-25
Consider the polynomial Division \(\displaystyle\frac{{{x}^{{3}}+{5}{x}^{{2}}-{7}{x}−{4}}}{{{x}−{2}}}\)

Answers (1)

2021-02-26
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.
0

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