1 / 15

Lesson 2.3 Real Zeros of Polynomials

Lesson 2.3 Real Zeros of Polynomials. The Division Algorithm. Dividing by a polynomial Set up in long division. 2 terms in divisor (x + 1). How does this go into 1 st two terms in order to eliminate the 1 st term of the dividend. 2x. + 1. Multiply by the divisor

Download Presentation

Lesson 2.3 Real Zeros of Polynomials

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. Lesson 2.3Real Zeros of Polynomials

  2. The Division Algorithm

  3. Dividing by a polynomial Set up in long division 2 terms in divisor (x + 1). How does this go into 1st two terms in order to eliminate the 1st term of the dividend. 2x + 1 • Multiply by the divisor • Write product under dividend • Subtract • Carry down next term • Repeat process - 2x2 + 2x - x + 5 - x + 1 - 4 Answer:

  4. HINTS: If a term is missing in the dividend – add a “0” term. If there is a remainder, put it over the divisor and add it to the quotient (answer) Example 1 (x4 – x2 + x) ÷ (x2 - x + 1)

  5. Synthetic Division • Less writing • Uses addition • Setting Up • Divisor must be of the form: x – a • Use only “a” and coefficients of dividend • Write in “zero terms” x – 2: a = 2 x + 3: a = -3 4 5 0 -2 5

  6. 4 5 0 -2 5

  7. Steps • Bring down • Multiply diagonally • Add • Remainder = last addition • Answer • Numbers at bottom are coefficients • Start with 1 degree less than dividend REPEAT

  8. Example 2: (2x3 – 7x2 – 11x – 20) (x – 5)

  9. Example 3: (2x4 – 30x2 – 2x – 1) (x – 4) Problem Set 2.3 (1 – 21 EOO)

  10. The Remainder Theorem If f(x) is divided by x – a , the remainder is r = f(a) The Factor Theorem If f(x) has a factor (x – a) then f(a) = 0

  11. Example 4 Show that (x – 2) and (x + 3) are factors of

  12. Rational Zero Test Every rational zero = Factors of constant term Factors of leading coefficient =

  13. Descartes’ Rule Number of positivereal roots is: ► the number of variations in the signs, or ► less than that by a positive even integer 5x4 – 3x3 + 2x2 – 7x + 1 variations: possible positive real roots:

  14. Example 5 List possible zeros, verify with your calculator which are zeros, and check results with Descartes’ Rule Problems Set 2.3

More Related