Question

If a polynomial function (x) has roots -2+√8 and 9, what must be a factor of (x)?

(x-(8-√2))

(x-(2-√8))

(x-(-2-√8))

(x-(-8+√2))

Answer 1

To find a factor of a polynomial function with given roots, if a number is a root of the function, then (x - root) is a factor of the function. The given roots are -2+√8 and 9, so the factors of the function are (x - (-2+√8)) and (x - 9). Simplifying the factors, we get (x + 2 - √8) and (x - 9). Therefore, the correct factor of (x) is (x - 9).

Step-by-step explanation:

To find a factor of a polynomial function with given roots, we use the fact that if a number is a root of the function, then (x - root) is a factor of the function. The given roots are -2+√8 and 9, so the factors of the function are (x - (-2+√8)) and (x - 9). Simplifying the factors, we get (x + 2 - √8) and (x - 9). Therefore, the correct factor of (x) is (x - 9).