Question
Divide the first polynomial by the second polynomial in the following. Also write the quotient and remainder: $\frac{10\text{x}^2-7\text{x}+8}{5\text{x}-3}$
✓
Answer
$\frac{10\text{x}^2-7\text{x}+8}{5\text{x}-3}$ $\frac{2\text{x}(5\text{x}-3)-\frac{1}{5}(5\text{x}-3)+\frac{47}{5}}{5\text{x}-3}$ $=\frac{(5\text{x}-3)\Big(2\text{x}-\frac{1}{5}\Big)(5\text{x}-3)+\frac{47}{5}}{5\text{x}-3}$ $=\Big(2\text{x}-\frac{1}{5}\Big)+\frac{\frac{47}{5}}{5\text{x}-3}$ Therefore, quotient $=\Big(2\text{x}-\frac{1}{5} \Big)$ and remainder $=\frac{47}{5}$
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