How do find the quotient of (y^3 - 125)/(y - 5)?

1 Answer
Oct 30, 2015

(y^2+5y+25)

Explanation:

You need to factor in order to get rid of the denominator. In order to do that you need to use the difference of cubes. That is

a3 + b3 = (a + b)(a2 – ab + b2)

a3 – b3 = (a – b)(a2 + ab + b2)

We are going to use the second one

Also a=y, b=5

Turn y^3 -125 to y^3 - 5^3

Use the formula

y^3 - 5^3=(y-5)(y^2+5y+25)

Plug that into the numerator

((y-5)(y^2+5y+25))/((y-5))

Simplify

(y^2+5y+25)