3x^5+x^4-17x^3-4x^2+20x divided by x^3-4x

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1 Answer

(3x5+x4-17x3-4x2+20x)/(x3-4x) simplifies to:

(3x4+x3-17x2-4x+20)/(x2-4) because x is a common factor.

          3x2+x-5                   (quotient)

x2-4 ) 3x4+x3-17x2-4x+20

        -(3x4     -12x2) 

                 x3  -5x2-4x

               -(x3        -4x)

                       -5x2     +20

                     -(-5x2     +20)

                              0 (no remainder)

CHECK

(x2-4)(3x2+x-5)=3x4+x3-5x2-12x2-4x+20=3x4+x3-17x2-4x+20.

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