POLYNOMIAL FUNCTIONS A POLYNOMIAL is a monomial or a sum of monomials. A POLYNOMIAL IN ONE VARIABLE is a polynomial that contains only one variable. Example: 5x 2 + 3x - 7

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POLYNOMIAL FUNCTIONS The DEGREE of a polynomial in one variable is the greatest exponent of its variable. A LEADING COEFFICIENT is the coefficient of the term with the highest degree. What is the degree and leading coefficient of 3x 5 – 3x + 2 ?

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POLYNOMIAL FUNCTIONS A polynomial equation used to represent a function is called a POLYNOMIAL FUNCTION . Polynomial functions with a degree of 1 are called LINEAR POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 2 are called QUADRATIC POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 3 are called CUBIC POLYNOMIAL FUNCTIONS

REMAINDER AND FACTOR THEOREMS f(x) = 3x 5 – 4x 3 + 5x - 3 Find f(-3) Try this one: Remember – Some terms are missing When synthetic division is used to evaluate a function, it is called SYNTHETIC SUBSTITUTION .

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REMAINDER AND FACTOR THEOREMS The binomial x – a is a factor of the polynomial f(x) if and only if f(a) = 0. FACTOR THEOREM

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REMAINDER AND FACTOR THEOREMS Is x – 2 a factor of x 3 – 3x 2 – 4x + 12 2 1 -3 -4 12 1 2 -1 -2 -6 -12 0 Yes, it is a factor, since f(2) = 0. Can you find the two remaining factors?

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REMAINDER AND FACTOR THEOREMS (x + 3)( ? )( ? ) = x 3 – x 2 – 17x - 15 Find the two unknown ( ? ) quantities.

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By: 5225ebp (65 month(s) ago)

nice presentation, it's simple, complete and clear. Students can easily understand this.