How to divide (x^3-8x^2+17x-10) -:(x-5)?

Serenity Colon

Serenity Colon

Answered question

2022-12-23

How to divide (x38x2+17x10)÷(x5)?

Answer & Explanation

blatt3qk

blatt3qk

Beginner2022-12-24Added 11 answers

\(\displaystyle\text{}{O}\ne{a}{p}{p}{r}{o}{a}{c}{h}{i}{s}\to{f}{a}{c}\to{r}{t}{h}{e}\div{i}{s}{\quad\text{or}\quad}\int{o}{t}{h}{e}\nu{m}{e}{r}{a}\to{r}.\text{}\)
\(\displaystyle\text{}{A}{n}{a}{l}{y}{z}{e}{t}{h}{e}\nu{m}{e}{r}{a}\to{r}\text{}\)
\(\displaystyle{\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{ma\genta}{+{5}{x}^{{2}}}}-{8}{x}^{{2}}+{17}{x}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{ma\genta}{-{15}{x}}}+{17}{x}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{red}{+{2}}}{\left({x}-{5}\right)}{\color{ma\genta}{+{10}}}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{red}{+{2}}}{\left({x}-{5}\right)}+{0}\)
\(\displaystyle\Rightarrow\frac{{{x}^{{3}}-{8}{x}^{{2}}+{17}{x}-{10}}}{{{x}-{5}}}\)
\(\displaystyle=\frac{{\cancel{{{\left({x}-{5}\right)}}}{\left({\color{red}{{x}^{{2}}-{3}{x}+{2}}}\right)}}}{\cancel{{{\left({x}-{5}\right)}}}}\)
\(\displaystyle={x}^{{2}}-{3}{x}+{2}\)

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