5.2A Evaluating Polynomial Functions

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E VALUATING P OLYNOMIAL F UNCTIONS A polynomial function is a function of the form f (x) = a n x n + a n – 1 x n – 1 +· · ·+ a 1 x + a 0 Where a n  0.

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Presentation transcript:

5.2A Evaluating Polynomial Functions Algebra II

Polynomial Function where , the exponents are all whole numbers, and the coefficients are all real numbers. For this polynomial function, is the leading coefficient, is the constant term, and n is the degree. A polynomial function is in standard form if its terms are written in descending order of exponents from left to right.

Common Types of Polynomial Functions Degree Type Standard Form

Identifying Polynomial Functions Ex. 1) Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type and leading coefficient. a.) b.)

Direct Substitution EX. 2)

Synthetic Substitution Ex. 3) Use synthetic division to evaluate when x = -2.

Evaluate by synthetic substitution without all parts Ex. 3b.)

Assignment

Evaluating a Polynomial Function in Real life Ex. 4) To disarm a business security panel, you must push 4 buttons, no two of which have the same number or letter. The total number of ways to set the system is modeled by where b is the number of buttons on the panel. Find how many ways the system can be set if there are 12 buttons on the panel.

Evaluate by Synthetic Substitution Ex. 3a.)