Classifying Polynomials

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Presentation transcript:

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 the exponents from greatest to least

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 No variable Constant 8x 1st degree Linear

Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant 8x 1st degree Linear 7x2 + 3x 2nd degree Quadratic

Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant 8x 1st degree Linear 7x2 + 3x 2nd degree Quadratic 6x3 – 2x 3rd degree Cubic

Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant 8x 1st degree Linear 7x2 + 3x 2nd degree Quadratic 6x3 – 2x 3rd degree Cubic 3x4 + 5x – 1 4th degree Quartic

Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant 8x 1st degree Linear 7x2 + 3x 2nd degree Quadratic 6x3 – 2x 3rd degree Cubic 3x4 + 5x – 1 4th degree Quartic 2x5 + 7x3 5th degree Quintic

Degree of a Polynomial (Each degree has a special “name”) 9 No variable Constant 8x 1st degree Linear 7x2 + 3x 2nd degree Quadratic 6x3 – 2x 3rd degree Cubic 3x4 + 5x – 1 4th degree Quartic 2x5 + 7x3 5th degree Quintic 5xn 6th degree or higher “nth” degree

Let’s practice classifying polynomials by “degree”. 3z4 + 5z3 – 7 15a + 25 185 2c10 – 7c6 + 4c3 - 9 2f3 – 7f2 + 1 15y2 9g4 – 3g + 5 10r5 –7r 16n7 + 6n4 – 3n2 DEGREE NAME Quartic Linear Constant Tenth degree Cubic Quadratic 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) terms Polynomial with 4 (or more) terms

Let’s practice classifying a polynomial by “number of terms”. 15x 2e8 – 3e7 + 3e – 7 6c + 5 3y7 – 4y5 + 8y3 64 2p8 – 4p6 + 9p4 + 3p – 1 25h3 – 15h2 + 18 55c19 + 35 Classify by # of Terms: Monomial Polynomial with 4 terms Binomial Trinomial Polynomial with 5 terms

Can you name them now? POLYNOMIAL 5x2 – 2x + 3 2z + 5 7a3 + 4a – 12 -15 27x8 + 3x5 – 7x + 4 9x4 – 3 10x – 185 18x5 CLASSIFICATION / NAME Quadratic Trinomial Linear Binomial Cubic Trinomial Constant Monomial 8th Degree Polynomial with 4 terms. Quartic Binomial Quintic Monomial