Given the degree, the real and imaginary solutions, and a point the graph goes through, I use the Linear Factorization Theorem to find the original polynomial function.
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In the last problem, the question would have to specify that the coefficients of the polynomial are real. Otherwise complex solutions don't necessarily have to occur in conjugate pairs. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob