find the greatest common factor and then factor problem

2x^8+4x^7-6x^6+4x^5

Question

find the greatest common factor and then factor problem

2x^8+4x^7-6x^6+4x^5

anonymous · Answer

$$2x ^{8}+4x ^{7}-6x ^{6}+4x ^{5}$$

anonymous · Answer

I know the GCF is 2 but I do not know how to do the rest

anonymous · Answer

I always start a problem like this by looking at the lowest x power. In this case, we see that is x^5. If we factor this out, we are left with
$$x^5 (2x^3+4x^2-6x+4)$$
Now we look at the coefficients. What's the highest number coefficient we can take out? Perhaps a 2?
$$2x^5 (x^3+2x^2-3x+2)$$
If you have any more questions feel free to ask!

anonymous · Answer

so would the last one be the answer to the factoring of the problem.

anonymous · Answer

Yes. You were correct in saying that the 2 could be factored out, but sometimes you have to be careful because there may be more terms (like the x^5 in this case).

Cheers!

anonymous · Answer

Thanks Chipperdrew are you going to be on here for a while I have a long ways to go on my assignment

anonymous · Answer

Not too long but I'll help you with what I can. Remember to always attempt to solve the problem on your own first, and then ask for questions. You learn much, much more that way!