Factoring Help?

Factor completely.

(x^2+6)^(7/2) + 2x(x^2+6)^(5/2) + x^2(x^2+6)^(3/2)

this is what I ended up with:

x^7 + 2x^6 + x^5 + x^2(6^1.5) + 2x(6^2.5) + 6^3.5

I think it could possibly be factored more but I’m not sure how. Thanks for any serious help.

Top 1 Answers

A few days ago

lomelinde

Favorite Answer

Actually, what you did was expand it. This is the opposite of factoring.

The first thing you should do is realize that each term has (x^2 + 6) ^ (7/2). So you pull that out and you have

[(x^2 + 6) ^ (7/2)] * (1 + 2x + x^2).

Then you can see that there is a perfect square, (1 + 2x + x^2). So you factor that and you get

[(x^2 + 6) ^ (7/2)] * (1 + x)^2

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