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Chapter 10 - Polynomials Tab 1: Identifying Polynomials.

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1 Chapter 10 - Polynomials Tab 1: Identifying Polynomials

2 Definition Polynomials : Is a monomial or a sum of monomials The prefix poly- means more than one, the suffix –nomial mean name but in math it means terms. Therefore, Polynomial means more than one term. Examples of Polynomials: * Terms are separated by a + or - sign. 2 12x³y 8x² + 4x – 3 x² - 9

3 Identifying Polynomials Polynomials are identified in two ways by the number of terms and by degree.

4 Identifying Polynomials by Terms Monomial: Mon means one, a polynomial with one term. Examples of Monomials: -4x 5 6x²y³

5 Identifying Polynomials by Terms * Terms are separated by a + or - sign. Binomial: Bi means two, a polynomial with two terms. Examples of Binomials: -4x + 3 x³- 225 6x²y³ - x

6 Identifying Polynomials by Terms * Terms are separated by a + or - sign. Trinomial: Tri means three, a polynomial with three terms. Examples of Trinomials: 8x² + 4x – 3 x²y³ + xy² – y 64y³ + y² – 2 * More than 3 terms is called a polynomial*

7 Identifying Polynomials by Degree Degree of the Polynomial is determined by the largest exponent of the variable. Examples: 5x³ + 4x² -6has a degree of 3Cubic x² + 4 has a degree of 2Quadratic 3x + 1 has a degree of 1Linear 2has a degree of 0Constant * More than a degree of 3, just write the number.*

8 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 6 3x + 1 -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

9 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60 3x + 1 -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

10 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60Constant 3x + 1 -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

11 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 1 -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

12 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11 -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

13 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11Linear -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

14 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-5 4x³ - 8x 5x³+4x²-6x+14

15 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52 4x³ - 8x 5x³+4x²-6x+14

16 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52Quadratic 4x³ - 8x 5x³+4x²-6x+14

17 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x 5x³+4x²-6x+14

18 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3 5x³+4x²-6x+14

19 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3Cubic 5x³+4x²-6x+14

20 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3CubicBinomial 5x³+4x²-6x+14

21 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3CubicBinomial 5x³+4x²-6x+143

22 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3CubicBinomial 5x³+4x²-6x+143Cubic

23 Let’s Put IT All Together PolynomialDegreeIdentify by Degree Identify by Terms 60ConstantMonomial 3x + 11LinearBinomial -x²+2x-52QuadraticTrinomial 4x³ - 8x3CubicBinomial 5x³+4x²-6x+143CubicPolynomial

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