happyfaces99
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synthetic division question


Why does the answer to \(\frac{x^3 +3x^2+11x+9}{x+1}\) not have a fraction under it... \((x^2+2x+9)\)

But \(\frac{2x^4-x^3-7x^2+7x+10}{x-2}\) have a fraction? \(2x^3+3x^2-1x+5+ \frac{25}{x-2}\)

Verified Answer :

\(\bf \cfrac{2x^4-x^3-7x^2+7x+10}{x-2}\\\\ -----------------------------\\\\ \begin{array}{llrrrrrrr} 2&|&2&-1&-7&7&10\\ &|&&4&6&-2&10\\ --&--&--&--&--&--&--&\\ &&2&3&-1&5&\boxed{20}&\leftarrow \textit{remainder} \end{array}\\\\ -----------------------------\\\\ 2x^3+3x^2-1x+5+\boxed{\frac{20}{x-2}}\)

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