End Behavior
What 2 things determine the end behavior of a polynomial graph?
Degree and Leading Coefficient
What 3 features do we need to sketch a graph?
X int, Y int, and End Behavior
How should you always write your remainder?
How do you know if something is a factor?
Remainder of zero
Factor
x^2+34x-35
(x+35)(x-1)
What is the difference between an even and odd degree graph?
Even the arrows go the same direction, odd they go opposite directions
How do you find the Y-int?
Always the constant!
When do you HAVE to use long division?
If the divisor has a coefficient on the X, or the degree is bigger than 1.
How do you know what numbers to guess when you use synthetic division?
They should be a factor of the constant.
Factor
x^4-225
(x^2-15)(x^2+15)
What about the leading coefficient affects the end behavior of a graph?
If it is a positive or negative number
How do you find the X ints?
Solve like normal
x^4-9x^3+17x^2+6x-33
divide x-6
x^3-3x^2+x-33/(x-6
Solve
x^3+2x^2-11x-12
x=3, x=-4, x=-1
Factor
3x^3-27x^2+42x
3x(x-2)(x-7)
What would the end behavior be for a polynomial with a degree of 4 and a LC of -3?
Negative Infinity for both
What information (besides end behavior) does the degree also tell you about your graph?
How many x-intercepts you should have.
4x^3+8x^2-9x+15
divide 2x+3
2x^2+x+6-3/(2x+3
Solve
x^3+7x^2+25x+175
x=-7, x=5i, x=-5i
Factor
x^4-6x^2+8
(x^2-2)(x+2)(x-2)
Give an example polynomial whose end behavior is negative on the left and positive on the right.
Odd degree and positive LC
4x^4-13x^3+7x-22
divide x-3
4x^3-x^2-3x-2-28/(x-3
x^4-x^3-2x^2-4x-24
x=3, x=-2, x=2i, x=-2i
Factor
x^3-343
(x-7)(x^2+7x+49)