divide the polynomial 3x2 - x3 - 3x+5 by the polynomial -x2+x-1 and verify the division algorithm
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divide the polynomial 3x2 - x3 - 3x+5 by the polynomial -x2+x-1 and verify the division algorithm
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also , -x^3+3x^2-3x+5
x^2+x-1 ) -x^3+3x^2-3x+5 ( -x+4
- x^3 -x^2+x
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4x^2-4x+5
4x^2 - 4x-4
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-8x+9
clearly , remainder = -8+9
quotient = -x+4
using division algorithm ,
a = b*q+r
= (x^2+x-1)(-x+4)-8+9
= -x^3+3x^2-3x+5
also , 3x^2-x^3-3x+5 ( dividend )