Divide (2x^2+17x+35)/(x+5)

$\frac{2 x^{2} + 17 x + 35}{x + 5}$

Step 1

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 $a \cdot c = 2 \cdot 35 = 70$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$\frac{2 x^{2} + 17 (x) + 35}{x + 5}$

Rewrite $17$ as $7$ plus $10$

$\frac{2 x^{2} + (7 + 10) x + 35}{x + 5}$

Apply the distributive property.

$\frac{2 x^{2} + 7 x + 10 x + 35}{x + 5}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x^{2} + 7 x) + 10 x + 35}{x + 5}$

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

$\frac{x (2 x + 7) + 5 (2 x + 7)}{x + 5}$

Factor the polynomial by factoring out the greatest common factor, $2 x + 7$ .

$\frac{(2 x + 7) (x + 5)}{x + 5}$

Step 2

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{(2 x + 7) (x + 5)}{x + 5}$

Divide $2 x + 7$ by $1$ .

$2 x + 7$

Divide (2x^2+17x+35)/(x+5)

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