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Monomials A real number, a variable or the product of a real number and one or more variables with whole number exponents. 3 Algebra 2 CP Polynomial A monomial or a sum of monomials x x4 Degree 3 x5 2 x3 3 A polynomial with the variable x defines the polynomial function of x. A polynomial function P(x) in standard form is: P x an x n an 1 x n 1 ... a1 x a0 of a Polynomial (in one variable) The greatest degree among the monomial terms. 4y descending terms by degree in ___________ numerical order 3x - degree 1 x 2 - degree 2 Degree 2 Arranges (in one variable) Exponent of the variable of a Monomial x2 3x x 4 - degree 1 x5 2 x3 3 where n is a nonnegative integer and an,…,a0 are real numbers. P x 4 x3 3x 2 5 x 2 - degree 5 Quadratic Term Cubic Term Linear Term Constant Term Write each polynomial in standard form. What is the classification of each by degree? By number of terms? Degree Name Using Degree 0 Constant 1 Linear 2 3 Quadratic Cubic 4 Quartic 5 Quintic 3x3 x 5 x 4 3 4 x5 2 x 2 10 Polynomial Example Number of Terms Name Using Number of Terms 5 x 4 3x3 x Standard Form: __________________ 4 x 2 x 13 Standard Form: __________________ 5 1 Monomial Classification Quartic (degree): _____________________ Classification Quintic (degree): _____________________ x4 2 Binomial Classification Trinomial (terms): _____________________ Classification Trinomial (terms): _____________________ Monomial 4 x3 2 x 2 x 1 3 2 x 5x 2 Binomial 4 Polynomial of 4 Terms 4x 4 2 2 x5 4 x 2 2 x 1 Trinomial 5 2 3x 4 x3 7 x 3 4x 4x 3 Standard Form: __________________ 3 Classification Cubic (degree): _____________________ Classification Trinomial (terms): _____________________ 1 n is even (n≠0) n is odd (n≠0) y 4 x3 2 x 2 7 a > 0 Rises to the left, Falls to the left, a<0 rises to the right rises to the right Falls to the left, Rises to the left, Falls to the right falls to the right 30 End Behavior: p x 4 x 4 4 x 3 24 x 2 x 6 End Behavior: 10 Turning Points: Rises to the left, rises to the right Turning Points: -10 20 10 Decreasing Interval: x -20 Decreasing Interval: -20 The function only decreases. -40 Increasing Interval: -10 Increasing Interval: -30 .02 x 2.14 1.41 x .02 Rises to the left, Falls to the right There are no turning points. 1.41, 16.1 .02, 6.01 2.14, 57.08 x 1.41 40 -30 -40 -50 x 2.14 -60 y x3 1 8 y x3 2 x 2 x 2 1. Make a table of values. 6 1. Make a table of values. 2. Plot points. 4 2. Plot points. x y -2 9 -1 2 0 1 1 0 2 7 2 x y -2 16 -1 2 0 2 1 2 -2 2 4 -4 4 -2 2 -2 2 -4 -6 -8 -4 -2 2 4 2