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