6x^4-7x^3+ax^2+3x+2能被x^2-x+b整除

As follows:

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2010-01-30 13:30:17 補充：
6x^4 – 7x^3 + ax^2 + 3x + 2 = (x^2 – x + b)(6x^2 + cx + m)
= 6x^4 – 6x^3 + 6bx^2 + cx^3 – cx^2 + bcx + mx^2 – mx + bm
= 6x^4 + (c – 6)x^3 + (6b – c + m)x^2 + (bc – m)x + bm
c – 6 = -7 => c = -1
a = 6b + 1 + m … (1)
3 = -b – m … (2)
bm = 2 … (3)

2010-01-30 13:30:40 補充：
(2) => b = -3 – m
Sub into (3), (-3 – m)m = 2
m^2 + 3m + 2 = 0
(m + 1)(m + 2) = 0
m = -1 or m = -2
m = -1 => b = -2 => a = -12 + 1 – 1 = -12
m = -2 => b = -1 => a = -6 + 1 – 2 = -7

thx你先
不過可5可以用意用(x^2-x+b)(6x+cx+m)做一次泥thx