SOLUTION: x(7x+5)^4(x+5)^2-5(7x+5)^3(x+5)^3-6x^2(7x+5)^3(7x+5)^3(x+5) I get the lcd of(7x+5)^3(x+5) but then I screw up the rest of the equation, can some kind soul please factor this mon

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x(7x+5)^4(x+5)^2-5(7x+5)^3(x+5)^3-6x^2(7x+5)^3(7x+5)^3(x+5) I get the lcd of(7x+5)^3(x+5) but then I screw up the rest of the equation, can some kind soul please factor this mon      Log On


   

Question 282858: x(7x+5)^4(x+5)^2-5(7x+5)^3(x+5)^3-6x^2(7x+5)^3(7x+5)^3(x+5)
I get the lcd of(7x+5)^3(x+5) but then I screw up the rest of the equation, can some kind soul please factor this monster and show me step by step so I can fiqure out where I am making my mistake. :|
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
First let's get some terminology straight. You're factoring out a GCF (Greatest Common Factor) not a LCD (Lowest Common Denominator). And this is an expression, not an equation.

Second, I am assuming that there is only supposed to be one %287x%2B5%29%5E3 near the end, not two consecutive ones.


You have correctly determined the GCF. First I will split up and rearrange some of the factors so the GCF will be more obvious:

I will use color-coding to help you see how this works. The GCF will be in red and the rest will be in green:

Now we can factor out the GCF (in red). Think of it as the Distributive Property "in reverse":

Now we try to factor the expression in green. In its current form I do not see any way to factor it so I'll simplify the expression:


red%28%287x%2B5%29%5E3%28x%2B5%29%29%28green%287x%5E3%2B29x%5E2-25x-125%29%29
The expression in green remains difficult to factor. I do not see how to factor by grouping and I've tested the possible rational roots and none of them work. So we have done as much factoring as possible (which means we are finished).