Question

Factorise $x^3-23x^2+142x-120$ by using factor theorem.

Answer 1

$x^3-x^2-22x^2+22x+120x-120$

$x^2(x-1)-22x(x-1)+120(x-1)$

$(x-1)(x^2-22x+120)$

$(x-1)(x^2-12x-10x+120)$

$(x-1)\left(x\right(x-12)-10(x-12\left)\right)$

$(x-1)(x-10)(x-12)$