Question
Divide the first polynomial by the second polynomial in the following. Also write the quotient and remainder: $\frac{3\text{x}^2+4\text{x}+5}{\text{x}-2}$
✓
Answer
$\frac{3\text{x}^2+4\text{x}+5}{\text{x}-2}$
$=\frac{3\text{x}(\text{x}-2)+10(\text{x}-2)+25}{\text{x}-2}$
$=\frac{3\text{x}(\text{x}-2)+10(\text{x}-2)+25}{\text{x}-2}$
$=\Big(3\text{x}+10\Big)+\frac{25}{\text{x}-2}$
Therefore, Quotient $= 3x + 10$ and reminder $= 25.$
$=\frac{3\text{x}(\text{x}-2)+10(\text{x}-2)+25}{\text{x}-2}$
$=\frac{3\text{x}(\text{x}-2)+10(\text{x}-2)+25}{\text{x}-2}$
$=\Big(3\text{x}+10\Big)+\frac{25}{\text{x}-2}$
Therefore, Quotient $= 3x + 10$ and reminder $= 25.$
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