Question

Factorise x cube + 1

Answer 1

Please see the attached answer

Answer 2

The correct answer is (x+1) and $x^{2} -x+1$.

Given: The equation = $x^{3}+1$.

To Find: Factors of this equation.

Solution:

Identity: $(x+1)^{3}=x^{3}+1+3x(x+1)$.

$x^{3}+1=(x+1)^{3}-3x(x+1)$

$x^{3}+1=(x+1)((x+1)^{2}-3x )$

$x^{3}+1=(x+1)(x^{2} +1+2x-3x )$

$x^{3}+1=(x+1)(x^{2} -x+1)$

Hence, the factors of $x^{3}+1$ are (x+1) and $x^{2} -x+1$.

#SPJ2