Advanced Algebra TASK - Classifying Polynomials Name: ________________________________ Date: ___________________ Period: _______ A polynomial is a mathematical expression involving a sum of nonnegative integer powers in one or more variables multiplied by coefficients. A polynomial in one variable with constant coefficients can be written in a n x n a n 1 x n 1 ...a 2 x 2 a1 x a 0 form where an 0 , the exponents are all whole numbers, and the coefficients are all real numbers. 1. What are whole numbers? 2. What are real numbers? 3. Decide whether each function below is a polynomial. If it is, write the function in standard form. If it is not, explain why. a. f ( x) 2 x 3 5x 2 4 x 8 b. f ( x) 2 x 2 x 1 c. f ( x) 5 x 7 x 3 x 2 d. f ( x) 2 2 x x 4 5 8x 3 e. f ( x) 2 x g. f ( x) 1 6 2 2 x 3x * A polynomial function in standard form is written in descending order of exponents from left to right. * The degree is the highest exponent and will help us classify the polynomial. * Coefficients are all real numbers. A leading coefficient is the number in front of the leading term when in standard form. * A constant term is a number without a variable. Ex. f(x) = 2 + 3x Ex. f(x) = 3x + x2 – 4 – 3x3 Standard Form: Degree: Leading Coefficient: Constant: Standard Form: Degree: Leading Coefficient: Constant: Classifying Polynomials by the number of terms: 1 Term: 2 Terms: Monomial Binomial 3 Terms: 4+ Terms: Trinomial Polynomial Classifying Polynomials by the degree: The degree of the polynomial is the same as the term with the highest degree. Degree of 0: Degree of 1: Degree of 2: Constant Linear Quadratic Degree of 3: Degree of 4: Degree of 5: Cubic Quartic Quintic Polynomial f ( x) 3 x 1 Number of Terms Classification Degree Classification f ( x) x 5 f ( x) 8x 3 125 f ( x) x 4 10 x 2 16 f ( x) x 2 2 x 1 f ( x) 2 Practice: State the degree and leading coefficient: Degree: LC: Degree: LC: Degree: LC: Degree: LC: Degree: LC: Degree: LC: Write the function in standard form and identify the following: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: Std Form: LC: Constant: Degree: # of Terms: Classify by Degree: Classify by Terms: