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Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

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Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

Objectives:

To determine left and right end behavior of a polynomial.

To find the zeros of a polynomial by factoring.

To determine the left and right end behavior of a polynomial we need to look at two things.

The leading coefficient of the function.

The degree of the function.

Recall xn and –xn.

- y = 3x2+4x-6
- y = -3x3+5x-8
- y = x5-4x3+5
- y = -2x4 + x3-2x2+6x-18
- y =(x-2)(x+1)(x+2)

If P is a polynomial and c is a real number, then the following are true.

- c is a zero of P.
- x = c is a solution of the equation P(x) = 0.
- x – c is a factor of P(x).
- x = c is an x-intercept of the graph of P.

- P(x) = x3 – 3x2 – 10x
- b) P(x) = x4 + x3 – 8x - 8

a)

b)

c)

Find the zeros and determine the end behavior.

1. P(x)= -2x(x – 6)

2. P(x) = 9x2 + 18x -7

3. P(x)= (x-3)(x+4)(x-8)(x+7)

4. P(x) = 2x3 - 4x2 – 16x