SOLUTION: Hello, I'd really appreciate it if you could help me with this problem. It's for an optional summer math packet for school. Solve the quadratic by factoring. 2x^3

SOLUTION: Hello, I'd really appreciate it if you could help me with this problem. It's for an optional summer math packet for school. Solve the quadratic by factoring. 2x^3 - 6x = 0

Question 149994: Hello,
I'd really appreciate it if you could help me with this problem. It's for an optional summer math packet for school.
Solve the quadratic by factoring.
2x^3 - 6x = 0
Found 2 solutions by scott8148, nerdybill:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
common factors first __ 2x(x^2-3)=0

factoring the remaining quadratic (difference of squares) __ 2x(x+sqrt(3))(x-sqrt(3))=0

2x=0 __ x=0

x+sqrt(3)=0 __ x=-sqrt(3)

x-sqrt(3)=0 __ x=sqrt(3)

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If you started with:
2x^3 - 6x = 0
A "common factor" for both terms is 2x -- pulling it out leaves:
(2x)(x^2 - 3) = 0
.
Looking at the above, if either (2x) OR (x^2 - 3), it will drive it to zero.
.
So, to find your solutions, set EACH term to zero and solve:
(2x)=0
x=0 (solution 1)
.
(x^2 - 3)=0
x^2 = 3
x = sqrt(3) (solution 2)
.
Therefore,
x = {0, sqrt(3)}
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