Question
Factorise the expression and divide them as directed: $\left(y^2+7 y+10\right) \div(y+5)$
✓
Answer
$\left(y^2+7 y+10\right) \div(y+5)$
$ = \frac{{{y^2} + 7y + 10}}{{y + 5}}$
$ = \frac{{{y^2} + 2y + 5y + 10}}{{y + 5}}$ . . . .[Using Identity $IV$
$ = \frac{{y(y + 2) + 5(y + 2)}}{{y + 5}}$
$ = \frac{{(y + 2)(y + 5)}}{{y + 5}}$
$= y + 2$
$ = \frac{{{y^2} + 7y + 10}}{{y + 5}}$
$ = \frac{{{y^2} + 2y + 5y + 10}}{{y + 5}}$ . . . .[Using Identity $IV$
$ = \frac{{y(y + 2) + 5(y + 2)}}{{y + 5}}$
$ = \frac{{(y + 2)(y + 5)}}{{y + 5}}$
$= y + 2$
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