Right answer:
C. g – 16
We can write every polynomial of degree [tex]n>0[/tex] with real coefficients as the product of linear and quadratic factors with real coefficients, where the quadratic factors have no real zeros. Here we have that:
[tex]g^2-32g+256[/tex]
So our goal is to find a factor of this. Factoring out, we need to find two numbers such that the product is 256 and the sum is -32. These two numbers are -16 and -16 again, because:
[tex](-16)(-16) = 256 \\ \\ -16 - 16 = -32[/tex]
So:
[tex]g^2-32g+256 = (g-16)(g-16)[/tex]
In fact, [tex](g-16)[/tex] is a factor of [tex]g^2-32g+256[/tex]
