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