Answer:
Option A is correct
[tex](x+6)(x+6)[/tex]
Step-by-step explanation:
To find the factor of the polynomial:
[tex]x^2-12x+36[/tex]
Consider the perfect square:
[tex](x \pm a)^2 = x^2 \pm 2ax+ a^2[/tex]
Compare this to [tex]x^2-12x+36[/tex]
⇒[tex]a^2 = 36[/tex]
⇒[tex]a =\pm\sqrt{36}=\pm 6[/tex]
Let a = -6
then;
[tex]2ax = 2 \cdot -6 \cdot x =-12x[/tex]
⇒[tex]x^2-12x+36 = (x-6)^2[/tex]
Using identity rule:
[tex](x-a)^2 = (x-a)(x-a)[/tex]
then;
[tex]x^2-12x+36 = (x-6)(x-6)[/tex]
Therefore, the factor of [tex]x^2-12x+36[/tex] is, [tex](x-6)(x-6)[/tex]
