How to divide (x^3-8x^2+17x-10) -:(x-5)?
Serenity Colon
Answered question
2022-12-23
Answer & Explanation
blatt3qk
Beginner2022-12-24Added 11 answers
\(\displaystyle\text{}{A}{n}{a}{l}{y}{z}{e}{t}{h}{e}\nu{m}{e}{r}{a}\to{r}\text{}\)
\(\displaystyle{\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{ma\genta}{+{5}{x}^{{2}}}}-{8}{x}^{{2}}+{17}{x}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{ma\genta}{-{15}{x}}}+{17}{x}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{red}{+{2}}}{\left({x}-{5}\right)}{\color{ma\genta}{+{10}}}-{10}\)
\(\displaystyle={\color{red}{{x}^{{2}}}}{\left({x}-{5}\right)}{\color{red}{-{3}{x}}}{\left({x}-{5}\right)}{\color{red}{+{2}}}{\left({x}-{5}\right)}+{0}\)
\(\displaystyle\Rightarrow\frac{{{x}^{{3}}-{8}{x}^{{2}}+{17}{x}-{10}}}{{{x}-{5}}}\)
\(\displaystyle=\frac{{\cancel{{{\left({x}-{5}\right)}}}{\left({\color{red}{{x}^{{2}}-{3}{x}+{2}}}\right)}}}{\cancel{{{\left({x}-{5}\right)}}}}\)
\(\displaystyle={x}^{{2}}-{3}{x}+{2}\)
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