Question

Which of the following represents the factorization of the trinomial below?x2 - 6x +9A. (x-2)(x-3)B. (x+2)(x-3)C. (x-3)D. (x+3)

Answer 1

$x^2-6x+9$

we have a trinomial

$a^2+2ab+b^2$

where

a=x

b=-3

Now, the way to factorize this trinomial is

$a^2+2ab+b^2=(a+b)^2$

replace the values

$\begin{gathered} a^2+2ab+b^2=(a+b)^2 \\ a=x,\text{ b=-3} \\ x^2+2(x)(-3)+(-3^2)=(x-3)^2 \\ x^2-6x+(9)=(x-3)^2 \\ \\ so,answer=(x-3)^2 \end{gathered}$