Right answer:
C. g – 16
We can write every polynomial of degree \(n>0\) 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:
\(g^2-32g+256\)
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:
\((-16)(-16) = 256 \\ \\ -16 - 16 = -32\)
So:
\(g^2-32g+256 = (g-16)(g-16)\)
In fact, \((g-16)\) is a factor of \(g^2-32g+256\)
