6y2+11y+43y2+7y+4

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅4=24 and whose sum is b=11.

Factor 11 out of 11y.

6y2+11(y)+43y2+7y+4

Rewrite 11 as 3 plus 8

6y2+(3+8)y+43y2+7y+4

Apply the distributive property.

6y2+3y+8y+43y2+7y+4

6y2+3y+8y+43y2+7y+4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6y2+3y)+8y+43y2+7y+4

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

3y(2y+1)+4(2y+1)3y2+7y+4

3y(2y+1)+4(2y+1)3y2+7y+4

Factor the polynomial by factoring out the greatest common factor, 2y+1.

(2y+1)(3y+4)3y2+7y+4

(2y+1)(3y+4)3y2+7y+4

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⋅4=12 and whose sum is b=7.

Factor 7 out of 7y.

(2y+1)(3y+4)3y2+7(y)+4

Rewrite 7 as 3 plus 4

(2y+1)(3y+4)3y2+(3+4)y+4

Apply the distributive property.

(2y+1)(3y+4)3y2+3y+4y+4

(2y+1)(3y+4)3y2+3y+4y+4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2y+1)(3y+4)(3y2+3y)+4y+4

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

(2y+1)(3y+4)3y(y+1)+4(y+1)

(2y+1)(3y+4)3y(y+1)+4(y+1)

Factor the polynomial by factoring out the greatest common factor, y+1.

(2y+1)(3y+4)(y+1)(3y+4)

(2y+1)(3y+4)(y+1)(3y+4)

Cancel the common factor.

(2y+1)(3y+4)(y+1)(3y+4)

Rewrite the expression.

2y+1y+1

2y+1y+1

Simplify (6y^2+11y+4)/(3y^2+7y+4)