SOLUTION: Show that -4 is a zero of multiplicity two of the function y=x^4+9x^3+23x^2+8x-16.

Question 1018711: Show that -4 is a zero of multiplicity two of the function y=x^4+9x^3+23x^2+8x-16.
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Can synthetic division by applied twice in succession and give remainder 0 for both of them?

That means, using synthetic division exactly two times in succession to "check the root, -4", will give 0 remainder, exactly those two times.

-4   |   1    9    23    8     -16
     |       -4   -20   -12     16
     |_________________________________
         1   5     3     -4     0


-4   |    1     5    3    -4
     |         -4    -4    4
     |____________________________
          1     1    -1    0


-4    |    1    1    -1
      |        -4    12
      |_______________________
           1   -3    11


-4 is a zero of the function shown at multiplicity 2.

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