Question

What is the factored form of x³-1?

(x³-1)(x²+x+1)
(x-1)(x²-x+1)
(x-1)(x²+x+1)
(x³-1)(x²+2x+1)

Answer 1

• 
  `\sf C.\; \sf \left(x-1\right)\left(x^2+x+1\right)`

Explanation:

`\sf x^3-1`

Let's rewrite 1 as 1 ^3.

`\sf x^3-1^3`

Now, we can apply the "Difference of Cubes Formula".

`\boxed{\sf x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)}`

• 
  `\sf x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)`

• 
  `\sf \left(x-1\right)\left(x^2+x+1\right)`

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