# Factor ((2y^2-3y-5)/(4y^2-25))÷((y^2-6y-7)/(2y^2-9y-35)) 2y2-3y-54y2-25÷y2-6y-72y2-9y-35
Factor by grouping.
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
Reduce the expression (y+1)(2y-5)(2y+5)(2y-5) by cancelling the common factors.
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
Factor y2-6y-7 using the AC method.
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
Factor by grouping.
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)
Reduce the expression (y-7)(y+1)(2y+5)(y-7) by cancelling the common factors.
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 by cancelling the common factors.
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))

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