a.Prove that if p(x) is a polynomial of an odd degree, then it must have atleast one real root.
b.Prove that if x0 is a root of ann-degree polynomial p(x), the polynomialcan be factored into
p(x)=(x−x0)q(x),
where q(x) is a polynomial of degreen−1.Explain what significance thistheorem has for finding the roots of a polynomial.
c.Prove that if x0 is a root of ann-degree polynomialp(x),then
p′(x0)=q(x0),
where q(x) is the quotient of the division of p(x) by x−x0.
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