Question
Factorise:
$x^3-x^2+a x+x-a-1$
$x^3-x^2+a x+x-a-1$
✓
Answer
$x^3-x^2+a x+x-a-1$
$=x^3-x^2+a x-a+x-1$
$=x^2(x-1)+a(x-1)+1(x-1)$
$=(x-1)\left(x^2+a+1\right)$
$=x^3-x^2+a x-a+x-1$
$=x^2(x-1)+a(x-1)+1(x-1)$
$=(x-1)\left(x^2+a+1\right)$
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