If f(x) is a polynomial function, then the values of x for which f(x) = 0 are called the zeros of the function. Graphically, these are the x intercepts

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Polynomial

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a mathematical expression involving a sum of nonnegative integer powers in one or more variables multiplied by coefficients. A polynomial in one variable with constant coefficients can be written in form

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Synthetic Division

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Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form (x - a). It can be used in place of the standard long division algorithm.

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Roots

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solutions to polynomial equations

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Fundamental Theorem of Algebra

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every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity.

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Remainder Theorem

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states that the remainder of a polynomial f(x) divided by a linear divisor
(x - c) is equal to f(c).

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Coefficient

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a number multiplied by a variable

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Polynomial

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a mathematical expression involving a sum of nonnegative integer powers in one or more variables multiplied by coefficients. A polynomial in one variable with constant coefficients can be written in form

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End Behavior

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the value of f(x) as x approaches positive and negative infinity

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Degree

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the greatest exponent of its variable

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Relative Minimum

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a point on the graph where the function is increasing as you move away from the point in the positive and negative direction along the horizontal axis.

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Polynomial

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Pascal's Triangle

Front

an arrangement of the values of nCr in a triangular pattern where each row corresponds to a value of n

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Multiplicity

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the number of times a root occurs at a given point of a polynomial equation.

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Relative Maximum:

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a point on the graph where the function is decreasing as you move away from the point in the positive and negative direction along the horizontal axis

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Rational Root Theorem

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a theorem that provides a complete list of all possible rational roots of a polynomial equation. It states that every rational zero of the polynomial equation ,where all coefficients are integers, has the following form: