3r2+5ry-2y2

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-2=-6 and whose sum is b=5.

Reorder terms.

3r2-2y2+5ry

Reorder -2y2 and 5ry.

3r2+5ry-2y2

Factor 5 out of 5ry.

3r2+5(ry)-2y2

Rewrite 5 as -1 plus 6

3r2+(-1+6)(ry)-2y2

Apply the distributive property.

3r2-1(ry)+6(ry)-2y2

Remove unnecessary parentheses.

3r2-1ry+6(ry)-2y2

Remove unnecessary parentheses.

3r2-1ry+6ry-2y2

3r2-1ry+6ry-2y2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3r2-1ry)+6ry-2y2

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

r(3r-1y)+2y(3r-y)

r(3r-1y)+2y(3r-y)

Factor the polynomial by factoring out the greatest common factor, 3r-1y.

(3r-1y)(r+2y)

(3r-1y)(r+2y)

Rewrite -1y as -y.

(3r-y)(r+2y)

Factor 3r^2+5ry-2y^2