Factorise completely x³ - 4x?

x³ - 4x
= x(x²-4)
= x(x²-2²)
= x(x+2)(x-2)

This can be solved by 2 ways. The first way is by taking x as a common factor, then:
x(x^2-4)
then factorize a^2 - b^2 = (a+b)(a-b)
x(x-2)(x+2).
the other way is by taking it as a polynomial of 3rd degree,
Take 2 as a root and by euclidean division ( long division) you wil have 0 and -2 next to 2

x³ - 4x
= x(x^2 - 4) ==> Remove their Highest Common Multiples
= x(x^2 - 2^2) ==> Take their common powers. (2^2=4)
= x [(x-2)^2] ==> Open up the brackets...
= (x)(x-2)(x-2) ==> Here's the answer!

Take out the common factor (x)

x(x^2-4)

Now its simply a difference of perfect square (DOPS)
Square root of 4 is 2

x(x-2)(x+2)

x(x+2)(x-2)

a^2 - b^2 = (a + b)(a - b)

x^3 - 4x
= x(x^2 - 4)
= x(x^2 - 2^2)
= x(x + 2)(x - 2)