6.1 (handout for Tuesday Jan 26)

6.1 (handout for Tuesday Jan 26) - 1 Constant Name Using...

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1 Section 6.1 Polynomial Functions Warm up s Multiply ) 1 )( 5 3 ( 2 - + x x x 3 ) 2 ( - x Objectives s Classify polynomials by degree and by number of terms s Write polynomials in standard form and factored form s But first, what is a polynomial? Definition of a Polynomial Function 0 1 1 1 .... ) ( a x a x a x a x P n n n n + + + + = - - s Where n is a nonnegative integer and the coefficients a n ……, a 0 are real numbers s The exponent of the variable determines the degree of the term. s When the terms are written in descending order by degree, the polynomial is in standard form. (also there must not be any two terms of the same degree) Example 12 2 5 ) ( 2 3 + + - = x x x x P Cubic term Leading Coefficient Quadratic term Linear term Constant term s We can classify a polynomial as a whole by both number of terms and degree (the degree of a polynomial is the largest degree of any one term) Quartic 4 Cubic 3 Quadratic 2 Quintic 5 Linear
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Unformatted text preview: 1 Constant Name Using Degree Degree Polynomial of 4 terms 4 Trinomial 3 Binomial 2 Monomial 1 Name Using Degree Number of terms Examples: 2 3 x 12 3 4 5 +-x x 2 You try – write each polynomial in standard form. Then classify it by degree and number of terms. y y 2 4 4-10 5 2 4 2 3---x x x Factored Form Vs. Standard Form s Just as all whole numbers can be written as the product of primes, all polynomials can be written as the product of linear factors. s When a polynomial has been factored completely into linear factors, it is in factored form. Write the polynomial in standard form STANDARD FORM FACTORED FORM ) 3 )( 2 )( 1 ( + + + x x x Write the polynomial in factored form STANDARD FORM FACTORED FORM x x x 12 10 2 2 3 + +...
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This note was uploaded on 05/13/2011 for the course MTH 98 taught by Professor Johnson during the Fall '09 term at Grand Valley State.

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6.1 (handout for Tuesday Jan 26) - 1 Constant Name Using...

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