Question

Write polynomial $P$ as a product of linear factors: $P\left(x\right)=-x^3-2x^2+5x+6$

Answer 1

We know that

$P\left(x\right)=-x^3-2x^2+5x+6$

Expanding the terms $-2x^2$ and $5x$

$\therefore P\left(x\right)=-x^3-x^2-x^2-x+6x+6$

Now taking the common terms

$P\left(x\right)=-x^2(x+1)-x(x+1)+6(x+1)$

$P\left(x\right)=(x+1)(-x^2-x+6)$

Solving $-x^2-x+6$

$P\left(x\right)=(x+1)(-x^2+2x-3x+6)$

$P\left(x\right)=(x+1)\left(x\right(-x+2)+3(-x+2\left)\right)$

$=(x+1)(2-x)(x+3)$