SOLUTION: Solve the following question by factoring. If need be submit as fraction to lowest terms. I don't understand these type problems 5z^8/3+4z^5/3-12z^2/3=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following question by factoring. If need be submit as fraction to lowest terms. I don't understand these type problems 5z^8/3+4z^5/3-12z^2/3=0      Log On


   

Question 718982: Solve the following question by factoring. If need be submit as fraction to lowest terms. I don't understand these type problems
5z^8/3+4z^5/3-12z^2/3=0
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


Factor out the smallest power of z:



Reduce the fraction exponents in the parentheses:

matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az%5E%282%2F3%29%28z%5E2%2B4z%5E1-12%29=0%29

Erase the 1 exponent:

matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az%5E%282%2F3%29%28z%5E2%2B4z-12%29=0%29

Factor the parentheses:

matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az%5E%282%2F3%29%28z%2B2%29%285z-6%29=0%29

Use the zero-factor property

matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az%5E%282%2F3%29=0%29     matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az%2B2=0%29     matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0A5z-6=0%29
matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0A+++++z=0%29         matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Az=-2%29     matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0A5z=6%29 

                      z=6%2F5

Edwin