Expert: Sherman D. - 5/30/2004

Question
I was asked to analyze the below graph, I'm truly stuck its due in two days and I have no clue where to start
-7x^8+6x^7+9x^6+4x^5-3x^4+3x^3-5x^2-6x-1
I was asked to find the range, domain, all maxs and mins, x intercepts and y intercepts, where the graph is increasing and decreasing, then I have to divide using long division by (x-2), and divide using synthetic division (x+4)  

Answer
to find the x-intercepts go to www.quickmath.com, click Solve(under equations), the type in
-7x^8 + 6x^7 + 9x^6 + 4x^5 - 3x^4 + 3x^3 - 5x^2 - 6x - 1
then click Solve, and you will get

x =
1
-.532253
-.208555
1.68964
-.780132 + .635518i
-.780132 + .635518i
.234288 - .835097i
.234288 + .835288i

To find y, i went to www.calculator.com, clicked on Graphing, then i got

y = -1

As for the rest, you will have to go to www.calculator.com

If this problem was no larger than x^4, then i could probably help you out there, but this is way to large for me to work out.

as for the last to things you needed, i get this


'''''''''-7x^7-8x^6-7x^5-10x^4-23x^3-43x^2 -91x-188 R -377
(x'-'2)/¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
'''''''''-7x^8+6x^7+9x^6+'4x^5-'3x^4+'3x^3-5x^2-'6x'''-''1
'''''''-'-7'''+14
'''''''-----------------
'''''''''''''''-8'''9
'''''''''''''-'-8' 16
''''''''''''-----------------
'''''''''''''''''''-7'''''4
''''''''''''''''-''-7''''14
'''''''''''''''----------------------
''''''''''''''''''''''''-10'''''-3
'''''''''''''''''''''-''-10'''''20
'''''''''''''''''''------------------------
'''''''''''''''''''''''''''''''-23''''''3
'''''''''''''''''''''''''''''-'-23'''''46
'''''''''''''''''''''''''''-----------------------
''''''''''''''''''''''''''''''''''''''-43'''''-5
''''''''''''''''''''''''''''''''''''- -43'''''86
'''''''''''''''''''''''''''''''''------------------------
'''''''''''''''''''''''''''''''''''''''''''''-91''''-6
'''''''''''''''''''''''''''''''''''''''''''-'-91'''182
''''''''''''''''''''''''''''''''''''''''-------------------
'''''''''''''''''''''''''''''''''''''''''''''''''''188'-'1
'''''''''''''''''''''''''''''''''''''''''''''''''-'188'376
'''''''''''''''''''''''''''''''''''''''''''''''------------
''''''''''''''''''''''''''''''''''''''''''''''''''''''-377


-7x^7 - 8x^6 - 7x^5 - 10x^4 - 23x^3 - 43x^2 - 91x - 188 R -377

or

-7x^7 - 8x^6 - 7x^5 - 10x^4 - 23x^3 - 43x^2 - 91x - 188 - (377/(x - 2))

If that doesn't turn out right, sorry, but hopefully you can understand what i meant.

---------------------------------

-4'|'-7''6''''9'''4''''-3''''3'''''-5'''''-6''|''''''-1
'''|''''28'-136'508'-2048'8204'-32828'131332''|'-525304    
--------------------------------------------------------
'''''-7'34'-127'512'-2051'8207'-32833'131326''|'-525305

-7x^7 + 34x^6 - 127x^5 + 512x^4 - 2051x^3 + 8207x^2 - 32833x + 131326 R -525305

or

-7x^7 + 34x^6 - 127x^5 + 512x^4 - 2051x^3 + 8207x^2 - 32833x + 131326 - (525305/(x + 4))

To let you know the '''' are to try and make my work not to become left aligned.

Sorry i couldn't help you on the other stuff. This problem is just larger than what i am use to.