Simplify (3x^2+7x-20)/(x+4)

$\frac{3 x^{2} + 7 x - 20}{x + 4}$

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 $a \cdot c = 3 \cdot - 20 = - 60$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{3 x^{2} + 7 (x) - 20}{x + 4}$

Rewrite $7$ as $- 5$ plus $12$

$\frac{3 x^{2} + (- 5 + 12) x - 20}{x + 4}$

Apply the distributive property.

$\frac{3 x^{2} - 5 x + 12 x - 20}{x + 4}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x^{2} - 5 x) + 12 x - 20}{x + 4}$

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

$\frac{x (3 x - 5) + 4 (3 x - 5)}{x + 4}$

Factor the polynomial by factoring out the greatest common factor, $3 x - 5$ .

$\frac{(3 x - 5) (x + 4)}{x + 4}$

Step 2

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{(3 x - 5) (x + 4)}{x + 4}$

Divide $3 x - 5$ by $1$ .

$3 x - 5$

Simplify (3x^2+7x-20)/(x+4)

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