Question

State True or False: $x^3-2x^2-x+2$$=(x-1)(x-2)(x+1)$

• A. True
• B. False

Answer 1

The correct option is A True

Let $p\left(x\right)=x^3-2x^2-x+2$
By trial, we find that
$p\left(1\right)=(1{)}^3-2(1{)}^2-\left(1\right)+2$
$=1-2-1+2=0$
$\therefore$ By factor Theorem (x-1) is a factor of p(x)
Now, $x^3-2x^2-x+2$
$=x^3-x^2-x^2+x-2x+2$
$=x^2(x-1)-x(x-1)-2(x-1)$
$=(x-1)(x^2-x-2)$
$=(x-1)(x^2-2x+x-2)$
$=(x-1)\left\{x\right(x-2)+1(x-2\left)\right\}$
$=(x-1)(x-2)(x+1)$