Chapter Polynomials of Higher Degree

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Presentation transcript:

Chapter 3 3.2 Polynomials of Higher Degree Obj – identify the end behaviors and zeros in order to graph a polynomial 3.3 Remainder and Factor Theorems Obj – use the synthetic formula to divide polynomial functions

3.2 Polynomials of Higher Degree Review: Degree = 0 y = c Degree = 1 y = mx + b Degree = 2 y =

Polynomials of Higher Degree Degree = 3 Degree = 4 Degree = 5 Degree = 6

Summarize If the degree is even, the end behaviors . . . If the degree is odd, the end behaviors . . . If the leading coefficient is positive, the right end behavior . . . If the leading coefficient is negative, the right end behavior . . .

Practice Determine the end behaviors.

Real Zeros of a Function Factor to find the real zeros. Real zeros are also the x-intercepts of the graph of the function. Use the end behaviors and the zeros to sketch the graph of the function.

Even and Odd Powers of (x-c) Theorem Use the graphing calculator to graph the polynomial Remember that the factors give the zeros or x-intercepts. If the power of the factor is odd, the graph . . . If the power of the factor is even, the graph . . .

Putting It All Together Sketch the graph of Factor to find the zeros. Find the y-intercept. Determine the end behaviors. Sketch.

3.3 Division of Polynomials Long Division or Synthetic Division Review:

Use the same process with polynomials. Divide Polynomials Use the same process with polynomials.

Synthetic Division Another process to divide polynomials IF you are dividing by a polynomial of form x – c. Rewrite: 2 1 3 4 -5

Practice Divide: Solve given that 2 is a zero.

The Remainder Theorem If a polynomial P(x) is divided by x – c, then the remainder equals P(c). Use synthetic division. The remainder is P(c).

The Factor Theorem A polynomial function P(x) has a factor (x – c) if and only if P(c) = 0. Determine whether the given binomial is a factor of P(x). Use synthetic division. If the remainder is zero, the binomial is a factor. Otherwise, the binomial is not a factor.

Assignment 3.2 20 – 30 by 5, 45 – 60 by 5, 3.3 1, 5, 9, 17, 21, 25, 33, 37, 41