SOLUTION: The expression x^4 + ax^3 + 5x^2 + bx + 6 when divide by (x-2), the remainder is 16 and then divided by (x+1) leaves remainder of 10. Find the value of a.

Question 1082142: The expression x^4 + ax^3 + 5x^2 + bx + 6 when divide by (x-2), the remainder is 16 and then divided by (x+1) leaves remainder of 10. Find the value of a.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

 2   1    a         5      b             6
          2      2a+4     4a+18   8a+2b+36
     -------------------------------------
     1    a+2    2a+9   4a+b+18   8a+2b+42

-1   1    a         5      b             6 
           -1    -a+1    a  -6     -a-b+ 6
     -------------------------------------
          a-1    -a+6    a+b-6     -a-b+12

     8a + 2b + 42 =  16
     -a -  b + 12 =  10

     8a + 2b      = -26
     -a -  b      = - 2

     8a + 2b      = -26
    -2a - 2b      = - 4

     6a           = -30
      a           = - 5

John

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

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