Section 6.2 and 6.3 Polynomials -- A function with several terms that are added or subtracted together, such as: 5x 4 + 3x 3 – 10x 2 + 17x – 9 10x 5 –

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Presentation transcript:

Section 6.2 and 6.3 Polynomials -- A function with several terms that are added or subtracted together, such as: 5x 4 + 3x 3 – 10x x – 9 10x 5 – 9x x x 2 – ½ x + 7 The degree of a polynomial is determined by the term with the largest exponent: 5x 4 + 3x 3 – 10x x – 9 is a 4 th degree polynomial. 10x 5 – 9x x x 2 – ½ x + 7 is a 5 th degree polynomial. 8x 4 y x 3 y + 4xy 2 this is actually a 6th degree polynomial, because the first term’s exponents combine to 6

More about Polynomials All exponents must be whole numbers f(x) = 5x 3 + 2x -1 These are not polynomials f(x) = 4x x Standard form of a Polynomial – arrange the terms left to right starting with the highest exponent: 7x x 4 – 12x x 2 – 9x x 5 + 7x 3 – 2x + 1

More about Polynomials Polynomials are named by how many terms they have: Monomial – one term…..7x Binomial – two terms…. 3x + 9 Trinomial – three terms… 7x 2 + 9x - 2 Polynomial – four or more terms… 4x 3 – 8x 2 + 6x + 12

Adding and Subtracting Polynomials Combine like terms with the same exponents Example: (10x 5 – 9x x x 2 – 4x + 7) + (5x 4 + 3x 3 – 10x x – 9) = 10x 5 – 4x x x x - 2

Multiplying Polynomials Use the distributive property, and remember your properties for exponents from Chapter x 6 (11x 3 – 6x 2 ) = 55x 9 – 30x 8 -7x 4 y 2 (2x 8 y 5 + 9x 3 y 4 ) = -14x 12 y 7 – 63x 7 y 6

Multiplying Polynomials Use FOIL for two Binomials (2x 2 + 3) (5x 4 + 9x) = 10x x x x Put in correct order: 10x x x x

Multiplying Polynomials (2x + 3) (5x + 7) (2x – 4) Use FOIL for the first two: = 10x x + 21 Then multiply: (10x x + 21) (2x – 4) = 20x 3 – 40x x 2 – 116x + 42x – 84 Simplify: = 20x x 2 – 74x - 84

Multiplying Larger Polynomials (5x + 6) (3x 2 + 7x + 4) Similar to using FOIL Multiply 5x by each term in the 2 nd polynomial 15x x x Then multiply 6 by each term in the 2 nd polynomial. 18x x + 24 Then combine the like terms and put in order: 15x x x + 42

Multiplying Larger Polynomials (9x 3 + 6x 2 + 2) (2x 2 -3x + 1) Multiply each term in the first equation by each term in the second equation = 18x 5 – 27x 4 + 9x x 4 -18x 3 + 6x 2 +4x 2 – 6x + 2 Combine like terms: = 18x 5 – 15x 4 – 9x x 2 – 6x + 2

Practice Page 341, #32,38,44