Classifying Polynomials Degree of a Polynomial The degree
- Slides: 18
Classifying Polynomials
Degree of a Polynomial The degree of a polynomial is calculated by finding the largest exponent in the polynomial. • In order for a function to be polynomial: • -leading coefficient must not be zero • -exponents must be whole numbers (no negatives • -no variables in the denominator **standard form of a polynomial function has
Degree of a Polynomial (Each degree has a special “name”) 9
Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant
Degree of a Polynomial (Each degree has a special “name”) 9 8 x No variable Constant 1 st degree Linear
Degree of a Polynomial (Each degree has a special “name”) 9 8 x 7 x 2 + 3 x No variable Constant 1 st degree Linear 2 nd degree Quadratic
Degree of a Polynomial (Each degree has a special “name”) 9 8 x 7 x 2 + 3 x 6 x 3 – 2 x No variable Constant 1 st degree Linear 2 nd degree Quadratic 3 rd degree Cubic
Degree of a Polynomial (Each degree has a special “name”) 9 8 x 7 x 2 + 3 x 6 x 3 – 2 x 3 x 4 + 5 x – 1 No variable Constant 1 st degree Linear 2 nd degree Quadratic 3 rd degree Cubic 4 th degree Quartic
Degree of a Polynomial (Each degree has a special “name”) 9 8 x 7 x 2 + 3 x 6 x 3 – 2 x 3 x 4 + 5 x – 1 2 x 5 + 7 x 3 No variable Constant 1 st degree Linear 2 nd degree Quadratic 3 rd degree Cubic 4 th degree Quartic 5 th degree Quintic
Degree of a Polynomial (Each degree has a special “name”) 9 8 x 7 x 2 + 3 x 6 x 3 – 2 x 3 x 4 + 5 x – 1 2 x 5 + 7 x 3 5 xn No variable Constant 1 st degree Linear 2 nd degree Quadratic 3 rd degree Cubic 4 th degree Quartic 5 th degree Quintic 6 th degree or higher “nth” degree
Let’s practice classifying polynomials by “degree”. 1. 2. 3. 4. 5. 6. 7. 8. 9. POLYNOMIAL 3 z 4 + 5 z 3 – 7 15 a + 25 185 2 c 10 – 7 c 6 + 4 c 3 - 9 2 f 3 – 7 f 2 + 1 15 y 2 9 g 4 – 3 g + 5 10 r 5 – 7 r 16 n 7 + 6 n 4 – 3 n 2 1. 2. 3. 4. 5. 6. 7. 8. 9. DEGREE NAME Quartic Linear Constant Tenth degree Cubic Quadratic Quartic Quintic Seventh degree The degree name becomes the “first name” of the polynomial.
Naming Polynomials (by number of terms)
Naming Polynomials (by number of terms) One term Monomial
Naming Polynomials (by number of terms) One term Monomial Two terms Binomial
Naming Polynomials (by number of terms) One term Monomial Two terms Binomial Three terms Trinomial
Naming Polynomials (by number of terms) One term Monomial Two terms Binomial Three terms Trinomial Four (or more) Polynomial with 4 (or more) terms
Let’s practice classifying a polynomial by “number of terms”. Polynomial 1. 2. 3. 4. 5. 6. 7. 8. 15 x 2 e 8 – 3 e 7 + 3 e – 7 6 c + 5 3 y 7 – 4 y 5 + 8 y 3 64 2 p 8 – 4 p 6 + 9 p 4 + 3 p – 1 25 h 3 – 15 h 2 + 18 55 c 19 + 35 1. 2. 3. 4. 5. 6. 7. 8. Classify by # of Terms: Monomial Polynomial with 4 terms Binomial Trinomial Monomial Polynomial with 5 terms Trinomial Binomial
Can you name them now? 1. 2. 3. 4. 5. POLYNOMIAL 5 x 2 – 2 x + 3 2 z + 5 7 a 3 + 4 a – 12 -15 27 x 8 + 3 x 5 – 7 x + 4 6. 9 x 4 – 3 7. 10 x – 185 8. 18 x 5 CLASSIFICATION / NAME 1. Quadratic Trinomial 2. Linear Binomial 3. Cubic Trinomial 4. Constant Monomial 5. 8 th Degree Polynomial with 4 terms. 6. Quartic Binomial 7. Linear Binomial 8. Quintic Monomial
- Classification of polynomials by degree
- Naming polynomials by degree
- Constant term
- Polynomial trinomial binomial monomial
- Classify each polynomial according to its degree and type.
- 7-5 polynomials
- Name of the polynomial
- Classifying polynomials
- Factoring is the process of
- Unit 6 polynomials and polynomial functions
- Review graphing polynomials
- How to divide a polynomial by another polynomial
- Matplotlib inline
- Factor higher order polynomials
- Cubic trinomial
- Constant polynomial
- What is the degree of linear polynomial
- Classify by degree
- Solving third degree polynomial