Question

One of the factors of g2 – 32g + 256 is:

A. g + 8

B. g – 8

C. g – 16

D. g + 16

Answer 1

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`

Answer 2

g^2 - 32g + 256 = (g - 16)(g - 16)...so ur answer is C. (g-16)