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 square6 Multiply ) 1 )( 5 3 ( 2 - + x x x 3 ) 2 ( - x Objectives square6 Classify polynomials by degree and by number of terms square6 Write polynomials in standard form and factored form square6 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 + + + + = - - square6 Where n is a nonnegative integer and the coefficients a n ……, a 0 are real numbers square6 The exponent of the variable determines the degree of the term. square6 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 square6 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
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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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