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2015-07-29T10:02:17+05:30

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The remainder of P(x) when divided by  x + 2  is obtained by  P(x= -2)

  = (-2)⁻⁴ - 4 (-2)³ + 3 (-2) -1
  = 41

we can do the division as :
quotient:  x³ - 6 x² + 12 x - 21

x+2  )    x⁴  - 4 x³  + 3 x  - 1  (  x³ - 6 x² + 12 x - 21
            x⁴  + 2 x³
           ========
                - 6 x³ + 3x
               - 6 x³ - 12 x²
               ===========
                       3x + 12 x²
                       24 x + 12 x²
                   ==============
                       -21 x  -1
                       -21 x  - 42
                       ============
                           41

===============================
A  simpler way of dividing the polynomial with x+2  is :
            
x + 2 )    1      -4        0        3       -1           
                     -2      12      -24      42
  ==============================
             1      -6       12      -21      41


So  quotient :  x³ - 6x² + 12 x - 21  and remainder  41

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