How many factors a polynomial of degree 5 can have?
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Since the degree of the polynomial is 5, it may have up to 5 real and imaginary roots according to the Fundamental Theorem of Algebra, so this list is valid. The remaining 2 roots must be either imaginary or lost in multiplicity. The final value is 0, therefore -2 is a root of the polynomial.
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Answer: since the degree of polynomial is 5 so it have 5real and imaginary roots
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