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October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Synthetic Division 3 2 Divide 2x - 3x - 5x - 12 by x - 3 using synthetic division. October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Rational Zeros Theorem: If there are rational zeros in the polynomial: f(x) = a x + an xn + ...n+ -a1 then they will be in the set n - 1 p q where p = factors of the constant, a and 0 q = factors of the leading term coefficient, a 0 October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Find the rational zeros of f(x) = 3x3 + 4x2 - 5x - 2 October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Upper and Lower Bound Tests for Real Zeros Suppose f(x) is divided by x - k using synthetic division. 1. If k≥ 0 and every number in the last line is nonnegative (pos. or zero), then k is an upper bound for the real zeros of f. 2. If k ≤ 0 and the numbers in the last line alternate nonnegative and nonpositive, then k is a lower bound for the real zeros of f. October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Prove that k = 5 is an upper bound for the real zeros of f(x) = 2x3 - 5x2 - 5x - 1 Prove that k = -4 is a lower bound for the real zeros of f(x) = 3x3 - x2 - 5x - 3 October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. Find the zeros. f(x) = x4 - x3 - 2x -4 October 19, 2015 Find the zeros. Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. f(x) = 2x4 - 7x3 - 8x2 + 14x + 8 October 19, 2015 Obj: To learn about Long Division of Polynomials, Remainder and Factor Theorems, Synthetic Division, Rational Zeros Theorem. HW (2.4) (HR) Pg.205: 2, 3, 7, 11, 13, 15, 19, 21, 27, 33, 35, 37, 41, 49, 51, 53