Question

y=2x^4-x^3-4x^2-x-6
-find max # of x-int
-find max # turning points
-all possible rational zeros
-synthetic division to list all possible rational zeros to determine function's x-int
-re-write in factored form
-use limit notation to state end behave
-sketch graph

Answer 1

@tcarroll010

Answer 2

so the only one I know how to do is #1 and #2...
I got 4 and 3 as my max

Answer 3

@jim_thompson5910

Answer 4

The possible rational zeros and the factors of 6 over the factors of 2

Answer 5

Did you finish this? @butterflyprincess

Answer 6

oh no!

Answer 7

@rajee_sam

Answer 8

possible rational zeros:
\[\pm \frac{6,3,2,1}{2,1}\]
i would start with smallest and check if its a zero w/ synthetic division

Answer 9

here is graph:
http://www.wolframalpha.com/input/?i=plot+2x%5E4-x%5E3-4x%5E2-x-6

you can see it looks like 2 may be a zero, so verify with synthetic division
then you can factor out (x-2)

2 | 2 -1 -4 -1 -6
4 6 4 6
-----------------
2 3 2 3 0

\[\rightarrow (x-2)(2x^{3} +3x^{2}+2x+3)\]
you can factor the rest w/ factor by grouping
\[\rightarrow (x-2)(x^{2} +1)(2x+3)\]
there are 2 x-int .... (-1.5,0) and (2,0)

the end behavior is f(x) -> pos infinity as x->+- infinity