Divide (2x^2+3x-14)/(x-2)

$\frac{2 x^{2} + 3 x - 14}{x - 2}$

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 $a \cdot c = 2 \cdot - 14 = - 28$ and whose sum is $b = 3$ .

Factor $3$ out of $3 x$ .

$\frac{2 x^{2} + 3 (x) - 14}{x - 2}$

Rewrite $3$ as $- 4$ plus $7$

$\frac{2 x^{2} + (- 4 + 7) x - 14}{x - 2}$

Apply the distributive property.

$\frac{2 x^{2} - 4 x + 7 x - 14}{x - 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x^{2} - 4 x) + 7 x - 14}{x - 2}$

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

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

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

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

Step 2

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

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

$2 x + 7$

Divide (2x^2+3x-14)/(x-2)

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