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Setting the Factors of a Polynomial Expression equal to zero gives the Solutions to the Equation when the polynomial expression equals zero. Another name for the Solutions of a Polynomial is the Roots of a Polynomial !

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…and the only way a product can equal zero is if one or more of the factors are zero…
We use the Fundamental Theorem. Of Algebra, Descartes Rule of Signs and the Complex Conjugate Theorem. to predict the nature of the roots of a polynomial.