SOLUTION: How to find the leading coefficient with graph provided? http://i.imgur.com/hslfSWo.png I know that it has 4 degrees and it looks like: P(x)=(x+3)(x+1)^2(x-2) but I just cant

Algebra ->  Graphs -> SOLUTION: How to find the leading coefficient with graph provided? http://i.imgur.com/hslfSWo.png I know that it has 4 degrees and it looks like: P(x)=(x+3)(x+1)^2(x-2) but I just cant      Log On


   

Question 916872: How to find the leading coefficient with graph provided?
http://i.imgur.com/hslfSWo.png
I know that it has 4 degrees and it looks like: P(x)=(x+3)(x+1)^2(x-2) but I just cant seem to figure out what the leading coefficient is I know it's negative since the graphing is downwards, does it have something to do with the y-intercept?
Please help!
Thanks
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


It has everything to do with the -intercept. The -intercept is the point where . So, if your polynomial is:



Then



and since we know from the graph that this value must be equal to 12, simply solve for where



John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=%28x%2B3%29%28x%2B1%29%5E2%28x-2%29 ... here you did use given roots correctly
P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6 ..this is expended form where the leading coefficient is highlight%281%29
but, you are also given y-intercept (0,12) we need 12
instead -6 in P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6
so, we need to multiply each term by -2 to get 12
then we have P%28x%29+=+highlight%28-2%29x%5E4-6x%5E3%2B6x%5E2%2B22x%2B12; the leading coefficient you are looking for is highlight%28-2%29

and as a product:
P%28x%29+=+-2%28x-2%29%28x%2B1%29%5E2%28x%2B3%29+