Answer :

Answer:

  f(x) = x³ -9x² +28x -30

Step-by-step explanation:

You want a monic polynomial f of least degree with zeros 3 and 3-i.

Factors

For zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...

  f(x) = (x -3)(x -3 +i)(x -3 -i)

  f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors

  f(x) = x³ -9x² +28x -30

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Additional comment

When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:

  f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)