SOLUTION: Hello I need some help with this problem: {{{4x^5-3x^3}}} I need to factor it into linear factors and find all the zeros (including complex zeros). I don't know how to factor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello I need some help with this problem: {{{4x^5-3x^3}}} I need to factor it into linear factors and find all the zeros (including complex zeros). I don't know how to factor      Log On


   

Question 40800: Hello I need some help with this problem:
4x%5E5-3x%5E3
I need to factor it into linear factors and find all the zeros (including complex zeros). I don't know how to factor this problem, I've tried doing this: x%5E3%284x%5E2-3%29 but I get stuck here. Can 0 be one of the zeros of this equation?
Answer by astromathman(21) About Me  (Show Source):
You can put this solution on YOUR website!
Yes. In fact 0 is a "tripple zero" of the function.
You can continue factoring using difference of two squares to get linear factors as required in the problem:
x%5E3%284x%5E2-3%29+=+x%5E3%282x%2Bsqrt%283%29%29%282x-sqrt%283%29%29. To get the zeros, set the whole expression equal to zero. Since the product equals zero, one of the factors equals zero, so set each factor equal to zero and solve for x. The zeros are:
0, -sqrt%283%29%2F2, and sqrt%283%29%2F2