SOLUTION: How do I determine the end behavior of the graph of the function? f(x)=-3x^6+2x^4+4x^3-2 How do I divide (3x^4-3x^3-6x-10)/(x-2) by using long division? How do I divide (4x^

Question 389687: How do I determine the end behavior of the graph of the function?
f(x)=-3x^6+2x^4+4x^3-2
How do I divide (3x^4-3x^3-6x-10)/(x-2) by using long division?
How do I divide (4x^4-12x^3-48x-60)/(x-4) by using long division?
For the function, use synthetic division and substitution to determine whether the given value is a zero of the function
P(x)=3x^4-10x^3-29x^2+16x+20, P(1)
How do I use substitution to determine whether x-3 is a factor of 4x^4-9x^3-109x^2+225x+225?

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!



  

Hi, Might recommend separately posting any other questions You may have

so as we as Tutors can best assist You further. 

dividing (3x^4-3x^3-6x-10)/(x-2) by using long division

          3x^3 + 3x^2 + 6x +6   Remainder = 2

    __________________________

x-2 |    3x^4  -3x^3  -6x-10

      - (3x^4 - 6x^3)

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

                3x^3   

             - (3x^3 - 6x^2)

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

                        6x^2 -6x

                      -(6x^2 -12x)

                          --------

                               6x -10

                             -(6x -12)

                              --------

                                   2

dividing (4x^4-12x^3-48x-60)/(x-4)done in similar fashion resulting in

4x^3 + 4x^2 + 16x + 16  Remainder = 4



As to: Using substitution to determine if an x value results in P(x) = 0

simply use that value of x in the function:

P(1)=3x^4-10x^3-29x^2+16x+20 = 3 -10 -29 + 16 + 20 = (29-29)= 0



As to using substitution to determine whether x-3 is a factor of 

4x^4-9x^3-109x^2+225x+225...(x-3) is a factor only if f(3) = 0

f(x) =4x^4-9x^3-109x^2+225x+225

f(3) = 4*81 - 9*27 - 109*9 + 255*3 + 225 = (1224 - 1224) = 0  (x-3) is a factor 

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