Question

How do you factor $x^3+1$?

Answer 1

Factorize using algebraic identity:

According to the algebraic identities,

$a^3+b^3=(\mathrm{a}+\mathrm{b})({\mathrm{a}}^2-\mathrm{ab}+{\mathrm{b}}^2)$

So, the given expression can be factorized as follows,

$x^3+1={\left(x\right)}^3+{\left(1\right)}^3$

$\Rightarrow x^3+1=\left(x+1\right)\left[{\left(x\right)}^2-x\times 1+{\left(1\right)}^2\right]$

$\Rightarrow x^3+1=\left(x+1\right)\left[x^2-x+1\right]$

$\Rightarrow x^3+1=\left(x+1\right)\left(x^2-x+1\right)$

Hence, the factors of $\left(x^3+1\right)$ obtained by using algebraic identity is $\left(x+1\right)\left(x^2-x+1\right)$.