SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials wi

Question 118101: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, if a polynomial has roots of a and b, then it's factorization will be

So if a polynomial has roots of -3, 4i, and -4i (remember complex roots always come in pairs) , then it's factorization will be

Rewrite as and as

Foil to get

Combine like terms

Replace with -1

Multiply

Now foil to get

So the polynomial with roots of -3 and +4i is
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