how to factor with a gcf

Question

i don't know how to do this problem

x²-6x+36

Answer 1

x^2-6x+36

has no integer factors, no common factors, no gcf

to see that:

set it equal to zero and solve for x, using either the quadratic formula or completing the square

x=6/2 +/-(1/2)(6^2 -4(1)36)= 3+/-.5sqr(-3(36)= 3+/-3isqr3

or complete the square

x^2-6x +9 = -36+9

(x-3)^2 = -27

x-3 = +/-isqr27 =+/-3isqr3

x = 3+/-3sqr3

x= 3+3isqr3 and 3-3isqr3

factors are x minus each zero above

x-3-3isqr3 and x-3+3isqr3

(x-3-3isqr3)(x-3+3isqr3) = x^2 -6x +36

but these are not integer factors,they're imaginary factors

"gcf" means greatest common factor

but more precisely it means greatest common integer factor

if the problem had been

x^2 -12x+36 = (x-6)^2

or

if it had been

x^2-6x+9 =(x-3)^2

with integer common factors