Question

Graph the polynomial $p\left(x\right)=x^3-6x^2+11x-6$ by finding zeros.

• A. $x=-1,2,3$
• B. $x=1,-2,3$
• C. $x=1,2,-3$
• D. $x=1,2,3$

Answer 1

Answer: (D)

$x=1,2,3$

$p\left(x\right)=x^3-6x^2+11x-6p\left(1\right)=1-6+11-6=0$

So $(x-1)$ is a factor of $p\left(x\right)$

Dividing $p\left(x\right)$ by $(x-1)$ we get

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

Factorising $q\left(x\right)$

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

So the zeroes of the polynomial are $x=1,2,3$

Option $D$ is correct