Mathematics - Lecture 16: Polynomial functions

Mathematics - Lecture 16 "Polynomial functions" presents the following content: Polynomial functions, synthetic division, remainder theorem and factor theorem, complex zeros, long division, theorem (division algorithm), remainder theorem, | Polynomial Functions Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 16 Math 17 (UP-IMath) Polynomial Functions Lec. 16 1 / 58 Outline 1 Polynomial Functions 2 Synthetic Division 3 Remainder Theorem and Factor Theorem 4 Complex Zeros Math 17 (UP-IMath) Polynomial Functions Lec. 16 2 / 58 Polynomial Functions Definition Let n ∈ W. A polynomial function of degree n is a function of the form p(x) = an xn + an−1 xn−1 + an−2 xn−2 + . . . + a1 x + a0 where a0 , a1 , ., an−2 , an−1 , an ∈ Math 17 (UP-IMath) R, and an = 0. Polynomial Functions Lec. 16 3 / 58 Polynomial Functions Definition Let n ∈ W. A polynomial function of degree n is a function of the form p(x) = an xn + an−1 xn−1 + an−2 xn−2 + . . . + a1 x + a0 where a0 , a1 , ., an−2 , an−1 , an ∈ R, and an = 0. Note: 1 We refer to an as the leading coefficient of p. Math 17 (UP-IMath) Polynomial Functions Lec. 16 3 / 58 Polynomial Functions Definition Let n ∈ W. A polynomial function of degree n is a function of the form p(x) = an xn + an−1 xn−1 + an−2 xn−2 + . . . + a1 x + a0 where a0 , a1 , ., an−2 , an−1 , an ∈ R, and an = 0. Note: 1 We refer to an as the leading coefficient of p. 2 We say a0 is the constant coefficient of p. Math 17 (UP-IMath) Polynomial Functions Lec. 16 3 / .