What is the quotient?

StartFraction 2 y squared minus 6 y minus 20 Over 4 y + 12 EndFraction divided by StartFraction y squared + 5 y + 6 Over 3 y squared + 18 y + 27 EndFraction

StartFraction 2 Over 3 (y minus 5) EndFraction

StartFraction 3 (y minus 5) Over 2 EndFraction

StartFraction (y minus 5) (y + 2) squared Over 6 (y + 3) squared EndFraction

StartFraction 3 (y + 5) (y minus 2) Over 2 (y + 2) EndFraction

Option B, 3 (y-5) / 2

StartFraction 3 (y minus 5) Over 2 EndFraction

Step-by-step explanation:

First we need to factor all the polynomials here using quadratic equation (-b + / - √ (b^2 - 4ac)) / 2a:

* 2y^2 - 6y - 20 = 2 (y^2 - 3y - 10)

From quadratic equation, solutions are 5 and - 2, which means that we can factor this to;

2 (y+2) (y-5)

* y^2 + 5y + 6, in the same manner, is found to have solutions - 3 and - 2, so it can be factored to:

(y+3) (y+2)

* 3y^2 + 18y + 27 = 3 (y^2 + 6y + 9)

Again, solving quadratic equation, we find solution to be - 3, so we factor this to:

3 (y+3) (y+3)

* 4y + 12 equals to 4 (y+3)

Now, let's rewrite our polynomials:

2 (y+2) (y-5) • 3 (y+3) (y+3) / 4 (y+3) • (y+3) (y+2)

We see that we can cancel out some factors here (x+3) and (x+2), so we are left with 6 (y-5) / 4 which is 3 (y-5) / 2.