Question

Find a polynomial f (x) of degree 3 that has the following zeros.
• -9, 1, 0
Leave your answer in factored form.

Answer 1

To construct a polynomial \( f(x) \) of degree 3 with the given zeros, we can use the fact that if \( r \) is a zero of a polynomial, then \( (x - r) \) is a factor of that polynomial.

The zeros you provided are -9, 1, and 0. This means the corresponding factors of the polynomial are:

- For the zero -9: \( (x + 9) \)
- For the zero 1: \( (x - 1) \)
- For the zero 0: \( (x - 0) = x \)

Putting these factors together, we get:

\[
f(x) = (x + 9)(x - 1)(x)
\]

Thus, the polynomial \( f(x) \) in factored form is:

\[
f(x) = x(x + 9)(x - 1)
\]