Simplify (2t^2+13t+15)÷(t+6)

$(2 t^{2} + 13 t + 15) \div (t + 6)$

Rewrite the division as a fraction.

$\frac{2 t^{2} + 13 t + 15}{t + 6}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 15 = 30$ and whose sum is $b = 13$ .

Factor $13$ out of $13 t$ .

$\frac{2 t^{2} + 13 (t) + 15}{t + 6}$

Rewrite $13$ as $3$ plus $10$

$\frac{2 t^{2} + (3 + 10) t + 15}{t + 6}$

Apply the distributive property.

$\frac{2 t^{2} + 3 t + 10 t + 15}{t + 6}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 t^{2} + 3 t) + 10 t + 15}{t + 6}$

Factor out the greatest common factor (GCF) from each group.

$\frac{t (2 t + 3) + 5 (2 t + 3)}{t + 6}$

Factor the polynomial by factoring out the greatest common factor, $2 t + 3$ .

$\frac{(2 t + 3) (t + 5)}{t + 6}$

Simplify (2t^2+13t+15)÷(t+6)

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