Question

question 2
find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): 3, - 2, 3. assume the leading coefficient is 1.
f(x)=
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Explanation:

Step1: Recall zero - factor property

If \(r\) is a zero of a polynomial, then \((x - r)\) is a factor.

Step2: Write factors for given zeros

For \(r_1 = 3\), \(r_2=-2\), \(r_3 = 3\), the factors are \((x - 3)\), \((x+2)\) and \((x - 3)\).

Step3: Form the polynomial

Since the leading coefficient is 1, \(f(x)=(x - 3)(x + 2)(x - 3)\).

Answer:

\(f(x)=(x - 3)^2(x + 2)\)