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) = x2 - 2x - x + 2
now take that and multiply by the last term
(x2 - 3x + 2)(x + 3)
(x2 - 3x + 2)(x + 3) =
x3 - 7x + 6
Write the expression (x + 1)(x + 2)(x + 3) in standard form.
Answer
x3 +6x2 +11x + 6
How do you factor things to the third power?
P(x) = 2x3 +10x2 +12x
What does every term have in common?
2x(x2 + 5x + 6)
now the first part is taken care of, but we need to simplify
the x2 + 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=0
x+3=0
or
2x - 3 = 0
or
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) = x4 +6x3 + 8x2
and state any multiplicity of them.
What do they all have in common?
P(x) = x2(x + 4)(x + 2)
zeros of
0 w/ mult 2
-4
-2
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!