Use the Division algorithm to find the quotient and remainderwhen f(x) is divide

Question

Use the Division algorithm to find the quotient and remainderwhen f(x) is divided by g(x) over the field of rational numbersQ. d) f(x) =2x4+x3-6x2-x+2,   g(x) =2x2-5 when I divide f(x) by g(x) I getg(x)(x2+.5x-.5)+((3/2)x-(5/2)). I think I amdone. Any feedback. Thanks. Use the Division algorithm to find the quotient and remainderwhen f(x) is divided by g(x) over the field of rational numbersQ. d) f(x) =2x4+x3-6x2-x+2,   g(x) =2x2-5 when I divide f(x) by g(x) I getg(x)(x2+.5x-.5)+((3/2)x-(5/2)). I think I amdone. Any feedback. Thanks.

Explanation / Answer

Your are correct!               x2 + x/2-1/2               -----------------   2x2-5)  2x4+x3-6x2-x+2,              2x4 + 0+-5x2               ---------------                        x3 -x2 -x                      x3+0 -5x/2                       -------------                            -x2+3x/2                             -x2+0 +5/2                          ------------                                    3x/2 -5/2 So  2x4+x3-6x2-x+2 =( 2x2-5). (x2 + x/2 - 1/2 ) + ( 3x/2 - 5/2)

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