Question

State True or False: $x^3-3x^2-9x-5$ $=(x+1)(x+1)(x-5)$

• A. True
• B. False

Answer 1

The correct option is A True

Let $p\left(x\right)=x^3-3x^2-9x-5$
By trial, we find that
$p(-1)=(-1{)}^3-3(-1{)}^2-9(-1)-5=-1-3+9-5=0$
$\therefore$ By factor Theorem (x+1) is a factor of p(x)
Now, $x^3-3x^2-9x-5=x^3+(x^2-4x^2)-(4x+5x)-5$
$=(x^3+x^2)-(4x^2+4x)-(5x+5)$
$=x^2(x+1)-4x(x+1)-5(x+1)$
$=(x+1)(x^2-4x-5)$
$=(x+1)(x^2-5x+x-5)$
$=(x+1)\left\{x\right(x-5)+1(x-5\left)\right\}$
$=(x+1)(x+1)(x-5)$