SOLUTION: solve by factoring given that (x+4) is one factor x^3+4x^2-16x-64=0

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Question 1063520: solve by factoring given that (x+4) is one factor
x^3+4x^2-16x-64=0
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Divide by x+4 using synthetic division.
-4    |    1    4    -16    -64
      |         -4   0      64
      |__________________________________
          1    0    -16     0


Equation now can be stated %28x%2B4%29%28x%5E2-16%29=0

%28x%2B4%29%28x%2B4%29%28x-4%29=0

system%28x=-4%2Cor%2Cx=4%29

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve by factoring given that (x+4) is one factor
x^3+4x^2-16x-64=0
~~~~~~~~~~~~~~~~~~~~~~

I can easily do it without this hint, simply applying grouping:

x%5E3+%2B+4x%5E2+-+16x+-+64 = %28x%5E3+%2B+4x%5E2%29 + %28-+16x+-+64%29 = x%5E2%28x%2B4%29 - 16%2A%28x%2B4%29 = %28x%2B4%29%2A%28x%5E2-16%29 = %28x%2B4%29%2A%28X%2B4%29%2A%28x-4%29 = %28x%2B4%29%5E2%2A%28x-4%29.

Hence, the original equation has the root x = -4 of multiplicity 2 and the root x = 4.