Simplify (3y^2+11y+15)/(2y^2+3y-20)

$\frac{3 y^{2} + 11 y + 15}{2 y^{2} + 3 y - 20}$

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 $a \cdot c = 2 \cdot - 20 = - 40$ and whose sum is $b = 3$ .

Factor $3$ out of $3 y$ .

$\frac{3 y^{2} + 11 y + 15}{2 y^{2} + 3 (y) - 20}$

Rewrite $3$ as $- 5$ plus $8$

$\frac{3 y^{2} + 11 y + 15}{2 y^{2} + (- 5 + 8) y - 20}$

Apply the distributive property.

$\frac{3 y^{2} + 11 y + 15}{2 y^{2} - 5 y + 8 y - 20}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{3 y^{2} + 11 y + 15}{(2 y^{2} - 5 y) + 8 y - 20}$

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

$\frac{3 y^{2} + 11 y + 15}{y (2 y - 5) + 4 (2 y - 5)}$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y - 5$ .

$\frac{3 y^{2} + 11 y + 15}{(2 y - 5) (y + 4)}$

Simplify (3y^2+11y+15)/(2y^2+3y-20)

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