SOLUTION: Factor the expression on the left side of each equation. Then solve the equation 4x³-32=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the expression on the left side of each equation. Then solve the equation 4x³-32=0      Log On


   

Question 263411: Factor the expression on the left side of each equation. Then solve the equation
4x³-32=0
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The original equation was
4x%5E3-32=0
step 1 - rewrite the left side as
%284%5E%281%2F3%29%5E3%29%2Ax%5E3+-+%282%5E%285%2F3%29%29%5E3+=+0
and then using difference of cubes, we get

set each part = 0 and solve to get
%284%5E%281%2F3%29%2Ax+-+2%5E%285%2F3%29%29+=+0
add 2^(5/3) to get
4%5E%281%2F3%29%2Ax+=+2%5E%285%2F3%29
divide by 4^(1/3) to get
x+=+2
the other parentheses, trinomial, will generate imaginary answers. so we get
x = 2.