Answer:
-2x + 5
Step-by-step explanation:
When you set this problem up:
[tex]\frac{125-8x^{3} }{25+10x+4x^{2} }[/tex]
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:
[tex]factor: -8x^{3} +125 = -(2x-5)(4x^2 +10x+25)[/tex]
WAIT! Look at the longer factor:
[tex]4x^2+10x+25[/tex]
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)
