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.