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the expression x-a is a linear factor of a polynomial if and only if the value of a is a zero of the related polynomial function
Fundamental Theorem of Algebra
if P(x) is a polynomial of degree n≥1 with complex coefficients, then P(x)=0 has at least one complex root
Imaginary Root Theorem
if the imaginary number a+bi is a root of a polynomial equation with real coefficients then the conjugate a-Bi is also a root
Irrational Root Theorem
Let a and b be rational numbers and let √b be an irrational number. If a+√b is a root of a polynomial equation with rational coefficients, then the conjugate a-√b is also a root
if a linear factor in a polynomial is repeated, the zero related to that factor is this
the number of times the related linear factor of a polynomial function is repeated in the factored form of the polynomial
the y-value of a point on the graph of a function that is higher than the nearby points of the graph
the y-value of a point on the graph of a function that is lower than the nearby points of the graph
if a polynomial P(x) of degree n≥1 is divided by (x-a), where a is a constant, then the remainder is P(a)
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