Question

Which of the binomials below is a factor of this trinomial? x^2 + 12x + 36A. x+6B. x-4C. x+4D. x-6

Answer 1

The trinomial is given to be:

`x^2+12x+36`

Rewrite the expression in the form:

`\begin{gathered} a^2+2ab+b^2 \\ 36=6^2 \\ 12x=2x\cdot6 \end{gathered}`

Therefore, the expression becomes:

`x^2+2x\cdot \:6+6^2`

Apply the perfect square formula:

`a^2+2ab+b^2=\left(a+b\right)^2`

Therefore, the expression becomes:

`\begin{gathered} a=x \\ b=6 \\ \therefore \\ x^2+2x\cdot6+6^2=(x+6)^2 \end{gathered}`

The correct option is OPTION A.