Thread: Factoring Question

I am trying to figure out how to factor out any common factors out of this polynomial: 4(x²+4)^3/2(3x+5)^1/3 + (3x+5)^4/3(x²+4)^1/23x
What I thought to do was to look for each base raised to the smallest exponent present in each term. Looking at the polynomial it looks like (3x+5)^1/3, and (x²+4)^1/2 are the bases raised to the lowest exponent because 3/2 > 1/2, and 4/3>1/3 therefore I tried to factor these out. When I try to do this I end up with 4(x²+4)^2/2+(3x+5)^3/33x[(3x+5)(x²+4)], and when I multiply the two binomials in the brackets I get 3x³+5x²+12x+20.
The answer in the text is (3x+5)^1/3(x²+4)^1/2(13x²+15x+16). I don't see how they arrived at this, and I also don't see how you could arrive at the original polynomial through multiplication of the terms in the answer. If someone could tell me what I am doing wrong, and explain how to arrive at the correct answer I would really appreciate it. Thanks a lot, I love this site.

There is a mistake in your simplification

It is (x^2+4)^(1/2) (3x+5)^(1/3) { 4(x^2+4) + 3x(3x+5)} This will give you the text answer.

Thanks for the reply, however I still don't understand how the bases raised to the 3/2, and 4/3 are less than the bases raised to the 1/3 and 1/2 (or then why if the bases (x2+4)^3/2, and (3x+5)^4/3 aren't less than the others why are they the terms that are factored out).

Originally Posted by KhanDisciple

Thanks for the reply, however I still don't understand how the bases raised to the 3/2, and 4/3 are less than the bases raised to the 1/3 and 1/2 (or then why if the bases (x2+4)^3/2, and (3x+5)^4/3 aren't less than the others why are they the terms that are factored out).

they're not ...

when you factor out from you get

check it by distributing the common factor

Thank you for clarifying skeeter, I see what I was doing wrong now.