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Division of a Polynomial by a Monomial

y2+7y+10÷ y+5...

Question

Evaluate $(y^{2} + 7 y + 10) \div (y + 5)$ .

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Solution

Given $(y^{2} + 7 y + 10) \div (y + 5)$ .
Since, $y^{2} + 7 y + 10 = y^{2} + 2 y + 5 y + 10$
$= y (y + 2) + 5 (y + 2)$
$= (y + 2) (y + 5)$
Thus, $\frac{y^{2} + 7 y + 10}{y + 5} = \frac{(y + 2) (y + 5)}{y + 5} = y + 2$

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