Question

A polynomial function has a zero at x=3 which of the follwing expressions must be one factor of the polynomial. A. x + 3 b. 3x C. x^3 D. x - 3 but could you explain how to do it so i can do it on my own! ...?

Answer 1

Answer: The correct option is (D) (x - 3).

Step-by-step explanation: Given that a polynomial function has a zero at x = 3.

We are to select the correct expression that must be a factor of the polynomial.

FACTOR THEOREM : The theorem states that if x = a is a zero of a polynomial p(x), then (x - a) will be a factor of the polynomial p(x).

In case of our given polynomial, since x = 3 is a zero of the polynomial, so by factor theorem, we can say that

(x - 3) is a factor of the given polynomial.

Thus, the required factor is (x - 3).

Option (D) is CORRECT.

Answer 2

I think the correct answer from the choices listed above is option D. A polynomial function has a zero value at x=3 for the expression where one factor is x-3. This factor when x=3 will always result to a zero value no matter what you multiply to it. Hope this answers the question.