Factorise:

Question:

Factorise:
x3 − 3x2 + x − 3

Solution:

We have:

$x^{3}-3 x^{2}+x-3=\left(x^{3}-3 x^{2}\right)+(x-3)$

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

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

$\therefore x^{3}-3 x^{2}+x-3=(x-3)\left(x^{2}+1\right)$

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