Some Factoring Problems! Help please!?

Question

There's only four, but they're tough in my opinion. I have a quiz tomorrow and I want to make sure I'm doing it right but there's no answer key. That is where you come in... and if you can show the steps that's be great! By the way this is for College Algebra Trig, so if you're not in that level yet, these may be too challenging. Unless you're a child genius or something. anyway, good luck! Thanks! here they are:

Factor Completely-

1. 2x^(4/3) + x^(1/3) (I think it factors to x^(1/3)(2x+1)?)

2. 4x^(2/5) + 2x^(1/5) + 6x^(6/5) (I think 2x^(1/5)(2x^(1/5) +1 +3x)

3. 8x^3 - 27x^(3/2) (I think x^(3/2)(2x^(1/2) -3)(4x +6x^(1/2) +9)

4. x^(5/2) -4x (I.... have no idea.)

Any help is greatly appreciated!

Answer 1

I did problems #1 and #2 on my own and got the same answers as you did. I'm not sure about #3 though.

Problem 4, here's what I did...

Remember that when you multiply two terms with the same base, you can add the exponents.

x^(5/2) -4x also equals x^(5/2) -4(x^5/2)(x^-4/2)

then

x^(5/2) * (1 - 4/(x^2))

then you have the difference of squares and it can be further simplified

x^(5/2) * (1 - 2/x)(1+2/x)