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}`