6.2 Factors of Polynomials Here are some graphs of different polynomials. Look at their end behavior and make some conjectures.

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Presentation transcript:

6.2 Factors of Polynomials Here are some graphs of different polynomials. Look at their end behavior and make some conjectures.

Relative mins and maxs What happens here and here?

You have a polynomial of degree 3 with zeros located at 2, -3, and 1. Write this polynomial in standard form.

P(x) = (x - 2)(x -1)(x + 3) start with the first two (x - 2)( x - 1)

(x - 2)(x - 1) = x 2 - 2x - x + 2 now take that and multiply by the last term (x 2 - 3x + 2)(x + 3)

x 3 - 7x + 6 (x 2 - 3x + 2)(x + 3) =

Write the expression (x + 1)(x + 2)(x + 3) in standard form.

Answer x 3 +6x 2 +11x + 6

How do you factor things to the third power? P(x) = 2x 3 +10x 2 +12x What does every term have in common?

2x(x 2 + 5x + 6) now the first part is taken care of, but we need to simplify the x 2 + 5x + 6 part. 2x( )( )

Find the zeros of P(x) = (x - 3)(2x - 3)(x + 3) and then graph. remember... zeros = solutions = roots x - 3 = 0or 2x - 3 = 0or x + 3 = 0

Write a polynomial with zeros of 2, 2, 0 P(x) = (x )(x )(x )

Find the zeros of (x + 3)(x +3)(3x - 7) Now you have three answers, but how many are distinct? This is called multiplicity.

Find the zeros of P(x) = x 4 +6x 3 + 8x 2 and state any multiplicity of them. What do they all have in common?

P(x) = x 2 (x + 4)(x + 2) zeros of 0 w/ mult

Do these problems as homework and also some on the board before we go. You are going to need to bring your A game everyday for the rest of the year in here. Hit up tutoring after school, use your online textbook tutorials, or come in early, lunch, after school. 15 extra minutes spent in school on math a day adds up to over an hour extra per week. PG. 317 # 5, 6, 7, 10, 12, 13, 18, 21, 22, 23, 29, 30, 31, 33, 35, 36, 37 = done CLEARLY on board before we can go!