MATH 041 Lecture Notes - Lecture 8: Coefficient, Algebraic Equation
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A polynomial function is of the form f(x) = anxn + an-1xn-1 + a1x + a0, x 0. The degree is the highest exponent, n. The graph of a polynomial function is continuous with no breaks. Power functions f(x) = anxn f(x) = x2 g(x) = x4 h(x) = -x6, n is even f(x) = x3 g(x) = x5 h(x) = -x7, n is odd. X = a, is a zero of the function f. X = a, is a solution of the polynomial equation f(x) = 0 (x a) is a factor of the polynomial f(x) (a, 0) is an x-intercept of the graph of f. X = 2 f(x) = (x 14) (x 5) (x 2) = (x2 5x 14x +70) (x 2) Maximum number of real zeros and maximum number of turning. Let f be a polynomial function of degree n. The function has at most n real zeros.
