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College Algebra K /DC Wednesday, 19 February 2014

College Algebra K /DC Wednesday, 19 February 2014. OBJECTIVE TSW use synthetic division to perform divisions. ASSIGNMENT DUE Sec. 3.1: p. 315 (52-55 all)  wire basket QUIZ: Sec. 3.1 is on Friday, 21 February 2014. Synthetic Division. 3.2. Synthetic Division.

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College Algebra K /DC Wednesday, 19 February 2014

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  1. College Algebra K/DCWednesday, 19 February 2014 • OBJECTIVETSW use synthetic division to perform divisions. • ASSIGNMENT DUE • Sec. 3.1: p. 315 (52-55 all)  wire basket • QUIZ: Sec. 3.1is on Friday, 21 February 2014.

  2. Synthetic Division 3.2 Synthetic Division

  3. Long Division of Polynomials • Use long division to divide .

  4. Synthetic Division • Use synthetic division to divide .

  5. Division Algorithm • Let f(x) and g(x) be polynomials with g(x) of lower degree than f(x), and let g(x) be of degree one or more. There exist unique polynomials q(x) and r(x) such that • f(x) = g(x) • q(x) + r(x), • where either r(x) = 0 or the degree of r(x) is less than the degree of g(x).

  6. Synthetic Division • Use synthetic division to divide .

  7. Remainder Theorem • What is f (–2) for f(x) = 5x3 – 6x2 – 28x – 2? f(−2) = 5(−2)3 – 6(−2)2 – 28(−2) – 2 = 5(−8)– 6(4) + 56 – 2 = −40 – 24 + 54 = −64 + 54 = −10 f (−2) = −10 Coincidence? I think not!!! r = −10

  8. Remainder Theorem • If the polynomial f (x) is divided by x – k, then the remainder is equal to f (k).

  9. Remainder Theorem • Use the Remainder Theorem to find f (4) for f (4) = 17

  10. Testing Potential Zeros • What is a zero of a polynomial? • ANSWER:Graphically, a zero is the x-value where the graph crosses the x-axis. • ANSWER:Algebraically, a zero is the x-value such that f(k) = 0. • If a number k is a zero of a polynomial, then f (k) = 0. zero zero zero

  11. Deciding Whether a Number is a Zero • Let . Is k = 2 a zero? 2 is a zero if f (2) = 0 (if the remainder = 0). Insert 0 as the coefficient for the missing x-term. NO: f (2) = −14, so k = 2 is NOT a zero. NOTE: When using synthetic division to decide if a given k is a zero, your answer will be YES or NO followed by the reason.

  12. Deciding Whether a Number is a Zero • Let . Is k = –3 a zero? YES: f (−3) = 0, so k = −3 is a zero.

  13. QUIZ on Friday, 21 February 2014 Covers Sec. 3.1 only • Find the vertex and axis of symmetry by • completing the square • using the vertex formula • State the domain and range. • Solve a projectile problem • Write the equation from the given information. • Memorize the general form.

  14. Assignment • Sec. 3.2: pp. 326-327 (1-7 odd, 8-18 even) • Write the problem; show all work. • Due on Friday, 21 February 2014.

  15. Class Problems: Sec. 3.2 [02/19/2014] wire basket • Use synthetic division to find each of the following. • Use the remainder theorem and synthetic division to find f(k). You have 25 minutes to finish. (Copy the problems before solving; I will change the slide in 15 minutes.)

  16. Assignment: Sec. 3.2: pp. 326-327 (1-7 odd, 8-18 even) Due on Friday, 21 February 2014. Use synthetic division to perform each division. QUIZ Sec. 3.1 will be on Friday, 21 February 2014.

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