Simplify (6w^3+7w^2-12w+15)/(2w^2+3w-5)

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w^{2} + 3 w - 5}$

Step 1

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 $a \cdot c = 2 \cdot - 5 = - 10$ and whose sum is $b = 3$ .

Factor $3$ out of $3 w$ .

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w^{2} + 3 (w) - 5}$

Rewrite $3$ as $- 2$ plus $5$

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w^{2} + (- 2 + 5) w - 5}$

Apply the distributive property.

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w^{2} - 2 w + 5 w - 5}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{(2 w^{2} - 2 w) + 5 w - 5}$

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

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w (w - 1) + 5 (w - 1)}$

Step 3

Factor the polynomial by factoring out the greatest common factor, $w - 1$ .

$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{(w - 1) (2 w + 5)}$

Simplify (6w^3+7w^2-12w+15)/(2w^2+3w-5)

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