Question

Divide $x^3-10x^2-53x-42$ by $x-3$.

Answer 1

$p\left(x\right)=x^3-10x^2-53x-42$

$p(-3)$ $={(-3)}^3-10{(-3)}^2-53\cdot (-3)-42=-27-90+159-42=0$

Thus $(x+3)$ is a factor of $p\left(x\right)$.

Now dividing $p\left(x\right)$ by $(x+3)$, we get

$(x^3-10x^2-53x-42)÷(x+3)=x^2-13x-14$

Therefore,

$p\left(x\right)$ $=(x+3)(x^2-13x-14)=(x+3)(x-14)(x+1)$

Hence

$x^3-10x^2-53x-42=(x+3)(x^2-13x-14)=(x+3)(x-14)(x+1)$