Question

What is the quotient (125-8x^3) divided by (25+10x+4x^2)

Answer 1

-2x + 5

Explanation:

When you set this problem up:

`(125-8x^(3) )/(25+10x+4x^(2) )`

It's easy to see that you can't really divide them due to their differing variables. So, we need to factor the numerator to give us equivalent variables:

`factor: -8x^(3) +125 = -(2x-5)(4x^2 +10x+25)`

WAIT! Look at the longer factor:

`4x^2+10x+25`

It is equivalent to our denominator! Now, that has made the job incredibly easier. Simply cancel out the like terms in the problem and we have our answer:

(-2x + 5)