it says write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed: -1 (multiplicity 2), -2 -i (multiplicity 1). Can anyone help?
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If you know the zero (root) of a function, you know a factor of it. Turn a zero into a factor by plugging the zero into (x - zero). For example, if 3 is a zero, then (x - 3) is a factor. Multiplicity just means how many times a particular factor is used. Multiplicity 2 means the factor is squared.
So, take all your factors (you'll have 3 in your example) and multiply them together (or just write them side by side if you don't need to FOIL out) and you're done.
There's one more thing you'll need. If a real polynomial has a complex root, say a + bi, then it also has the root a - bi, called the complex conjugate of a + bi.
So our polynomial actually has an additional root -2 + i,
which is stealthily hidden in the list they gave.