2y2-3y-54y2-25÷y2-6y-72y2-9y-35

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-5=-10 and whose sum is b=-3.

Factor -3 out of -3y.

2y2-3(y)-54y2-25y2-6y-72y2-9y-35

Rewrite -3 as 2 plus -5

2y2+(2-5)y-54y2-25y2-6y-72y2-9y-35

Apply the distributive property.

2y2+2y-5y-54y2-25y2-6y-72y2-9y-35

2y2+2y-5y-54y2-25y2-6y-72y2-9y-35

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2y2+2y)-5y-54y2-25y2-6y-72y2-9y-35

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

2y(y+1)-5(y+1)4y2-25y2-6y-72y2-9y-35

2y(y+1)-5(y+1)4y2-25y2-6y-72y2-9y-35

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

(y+1)(2y-5)4y2-25y2-6y-72y2-9y-35

(y+1)(2y-5)4y2-25y2-6y-72y2-9y-35

Rewrite 4y2 as (2y)2.

(y+1)(2y-5)(2y)2-25y2-6y-72y2-9y-35

Rewrite 25 as 52.

(y+1)(2y-5)(2y)2-52y2-6y-72y2-9y-35

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2y and b=5.

(y+1)(2y-5)(2y+5)(2y-5)y2-6y-72y2-9y-35

Cancel the common factor.

(y+1)(2y-5)(2y+5)(2y-5)y2-6y-72y2-9y-35

Rewrite the expression.

y+12y+5y2-6y-72y2-9y-35

y+12y+5y2-6y-72y2-9y-35

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -7 and whose sum is -6.

-7,1

Write the factored form using these integers.

y+12y+5(y-7)(y+1)2y2-9y-35

y+12y+5(y-7)(y+1)2y2-9y-35

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-35=-70 and whose sum is b=-9.

Factor -9 out of -9y.

y+12y+5(y-7)(y+1)2y2-9(y)-35

Rewrite -9 as 5 plus -14

y+12y+5(y-7)(y+1)2y2+(5-14)y-35

Apply the distributive property.

y+12y+5(y-7)(y+1)2y2+5y-14y-35

y+12y+5(y-7)(y+1)2y2+5y-14y-35

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

y+12y+5(y-7)(y+1)(2y2+5y)-14y-35

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

y+12y+5(y-7)(y+1)y(2y+5)-7(2y+5)

y+12y+5(y-7)(y+1)y(2y+5)-7(2y+5)

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

y+12y+5(y-7)(y+1)(2y+5)(y-7)

y+12y+5(y-7)(y+1)(2y+5)(y-7)

Cancel the common factor.

y+12y+5(y-7)(y+1)(2y+5)(y-7)

Rewrite the expression.

y+12y+5y+12y+5

y+12y+5y+12y+5

Reduce the expression y+12y+5y+12y+5 by cancelling the common factors.

Cancel the common factor.

y+12y+5y+12y+5

Rewrite the expression.

11

11

Rewrite the expression.

1

1

Factor ((2y^2-3y-5)/(4y^2-25))÷((y^2-6y-7)/(2y^2-9y-35))