Question

State True or False:

$x^3+13x^2+32x+20$ $=(x+1)(x+2)(x+10)$

• A. True
• B. False

Answer 1

The correct option is A True

Let $p\left(x\right)=x^3+13x^2+32x+20$
By trial, we find that
$p(-1)=(-1{)}^3+13(-1{)}^2+32(-1)+20=-1+13-32+20=0$
$\therefore$ By factor Theorem (x+1) is a factor of p(x)
Now, $x^3+13x^2+32x+20=x^3+(x^2+12x^2)+(12x+20x)+20$
$=(x^3+x^2)+(12x^2+12x)+(20x+20)$
$=x^2(x+1)+12x(x+1)+20(x+1)$
$=(x+1)(x^2+12x+20)$
$=(x+1)(x^2+10x+2x+20)$
$=(x+1)\left\{x\right(x+10)+2(x+10\left)\right\}$
$=(x+1)(x+2)(x+10)$