Question

Which of the following is a factor of $x^2+6x+9$?

• A. x + 8
• B. 8 - x
• C. x - 2
• D. x - 6

Answer 1

The correct option is B

8 - x

The expression $x^2+6x+9$ can be written as,

$=x^2+2\times x\times 3+3^2$...(i)

Comparing (i) with the identity $a^2+2ab+b^2=(a+b{)}^2$, we get

$a^2=x^2\Rightarrow a=x$

$b^2=3^2\Rightarrow b=3$

$\Rightarrow$ $x^2+6x+9$$=(x+3{)}^2$

Therefore, the factors of $x^2+6x+9$ are $(x+3)(x+3)$.