Question

Which of the following does not have $(x-3)$ as a factor?

• A. $x^2-3^2$
• B. $x^2-6x+9$
• C. $x^2+6x+9$
• D. ${(x+3)}^2-12x$

Answer 1

Answer: (C)

$x^2+6x+9$

Option A: $x^2-3^2=(x-3)(x+3)$ ...$[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$

Option B: $x^2-6x+9$

$={\left(x\right)}^2-2\left(x\right)\left(3\right)+{\left(3\right)}^2$ ...$[\because {(a-b)}^2=a^2-2ab+b^2]$

$={(x-3)}^2$

$=(x-3)(x-3)$

Option C: $x^2+6x+9$

$={\left(x\right)}^2+2\left(x\right)\left(3\right)+{\left(3\right)}^2$ ...$[\because {(a+b)}^2=a^2-2ab+b^2]$

$={(x+3)}^2$

$=(x+3)(x+3)$

Option D: $(x+3{)}^2-12x$

$=x^2+6x+9-12x$

$=x^2-6x+9$

$={(x-3)}^2$

$=(x-3)(x-3)$

$\therefore$ option C does not have $(x-3)$ as a factor.