Introduction to Polynomials 24 February 2011. What is a polynomial? polynomial.

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Presentation transcript:

Introduction to Polynomials 24 February 2011

What is a polynomial? polynomial

Definition of Polynomial A polynomial is algebraic expression that can be written in the form a n x n + a n-1 x n-1 + … + a 2 x 2 + a 1 x 1 + a 0 An equation or an expression with a single variable raised to (usually many) powers All exponents are whole numbers a n ≠ 0

Key Features of Polynomials a n x n + a n-1 x n-1 + … + a 2 x 2 + a 1 x 1 + a 0 Constant (the term without a variable) Leading Coefficient (a n ) Degree (n, greatest exponent in polynomial)

Notes About Polynomials Exponents can be skipped! Ex. 8x 8 – x 4 + 2x – 1 Written in numerical order from greatest exponent to least exponent Ex. 2x 3 + 7x 8 – 14x 2 – x 5 Rewrite: 7x 8 + 5x 5 + 2x 3 – 14x 2 – 12

Classifying Polynomials Classified according to key features Degree Leading Coefficient Constant Degree especially important!

Naming Polynomials Named according to their degree Ex. 3x x 5 – 11x 3 + 2x x – th degree polynomial Some polynomials have special names: 0 degree (just a constant term): Constant 1 st degree: Linear 2 nd degree: Quadratic 3 rd degree: Cubic 4 th degree: Quartic 5 th degree: Quintic

Examples: x 3 Degree: Name: 4x x 7 + 5x 2 – 7x Rewrite: Degree: Name:

Examples: 0x 9 + 2x 6 + 3x 7 + x 8 – 2x – 4 Rewrite: Degree: Name: 12 Degree: Name:

Your Turn: Complete the table on the Classifying Polynomials handout You may need to rewrite the polynomial 1 st !!!