1 / 10

MAT 150 – Class #23

MAT 150 – Class #23. Topics: Divide Polynomials with Long Division and Synthetic Division Solve Cubic and Quartic Equations Fundamental Theorem of Algebra Find Complex Solutions. Long Division . Synthetic Division. Divide. The weekly profit for a product, in thousands of dollars, is ,

desmondd
Download Presentation

MAT 150 – Class #23

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MAT 150 – Class #23 • Topics: • Divide Polynomials with Long Division and Synthetic Division • Solve Cubic and Quartic Equations • Fundamental Theorem of Algebra • Find Complex Solutions

  2. Long Division Synthetic Division Divide

  3. The weekly profit for a product, in thousands of dollars, is , where x is the number of thousands of units produced and sold. To find the number of units that give break even, Graph the function on the window [-10, 20] by [-100, 100]. Graphically find one x-intercept of the graph. Use synthetic division to find a quadratic factor of P(x). Find all of the zeros of P(x). Determine the levels of production and sale that give break-even. Break-Even (#34, Pg. 464)

  4. Break-EvenPart A/B

  5. Break-EvenPart C: Synthetic Division(PG. 455)

  6. Break-EvenPart D/E

  7. Rational Solutions Test (or Rational Root Test): The rational solutions of the polynomial equation With integer coefficients must be of the form where p is the factor of the constant term and q is a factor of , the leading coefficient. Example: Determine all possible rational solutions:

  8. Fundamental Theorem of Algebra : If f(x) is a polynomial function of degree , then f has a least one complex zero. Complex Zeros: Every polynomial function f(x) of degree has exactly n complex zeros. Some of these zeros may be imaginary, and so may be repeated. Nonreal zeros occur in conjugate pairs, a + bi and a – bi.

  9. Find all zeros of the polynomial functions and sketch the graph: Note: If a zero is repeated, occurs twice, then we say that zero has multiplicity.

  10. Pg. 463-465 #15,16, 23, 28, 29, 30 #33, 37, 38, 40 Assignment

More Related