Divide (6x^2-19x+10)/(2x-5)

$\frac{6 x^{2} - 19 x + 10}{2 x - 5}$

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 $a \cdot c = 6 \cdot 10 = 60$ and whose sum is $b = - 19$ .

Factor $- 19$ out of $- 19 x$ .

$\frac{6 x^{2} - 19 (x) + 10}{2 x - 5}$

Rewrite $- 19$ as $- 4$ plus $- 15$

$\frac{6 x^{2} + (- 4 - 15) x + 10}{2 x - 5}$

Apply the distributive property.

$\frac{6 x^{2} - 4 x - 15 x + 10}{2 x - 5}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x^{2} - 4 x) - 15 x + 10}{2 x - 5}$

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

$\frac{2 x (3 x - 2) - 5 (3 x - 2)}{2 x - 5}$

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$\frac{(3 x - 2) (2 x - 5)}{2 x - 5}$

Step 2

Cancel the common factor of $2 x - 5$ .

Cancel the common factor.

$\frac{(3 x - 2) (2 x - 5)}{2 x - 5}$

Divide $3 x - 2$ by $1$ .

$3 x - 2$

Divide (6x^2-19x+10)/(2x-5)

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