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Leading coefficient of a polynomial is the coefficient of the highest power of x.
Leading coefficient is inherently non-zero
Monic polynomials: leading coefficient == 1
Rational Root Theorem:
forall P(x): polynomial of degree n with integer coefficients
forall p, q: Z such that p/q is a root of P(x)
p is a factor of a[0]
q is a factor of a[n]