Question

Find all the zeros. SHOW ALL WORK!
5x^3 – 5x = 0

Thank you for your help :)

Answer 1

factor
remember
if xy=0, assume that x and y=0
also
difference of 2 perfect squares
a²-b²=(a-b)(a+b)

so
5x³-5x=0
factor out 5x
5x(x²-1)=0
5x(x²-1²)=0
factor perefect square
5x(x-1)(x+1)=0
set each to zero

5x=0
x=0

x-1=0
x=1

x+1=0
x=-1

x=-1 or 0 or 1