Question

What is the factored form of x^3-1

Answer 1

the factors of x^3-1 are
`x^3 -1 = (x-1) (x^2 +x+1)\\`

Explanation:

We need to find factors of x^3 -1

`x^3-1 \\(x)^3 -(1)^3\\We \,\, know\,\, a^3 -b^3 = (a-b) (a^2 +ab + y^2) \\So, \,\, using\,\, the \,\, formula\,\,\\Here\,\, a= x \,\,and\,\, b= 1\\(x)^3 -(1)^3 = (x-1) (x^2 +x+1)\\`

So, the factors of x^3-1 are
`x^3 -1 = (x-1) (x^2 +x+1)\\`