F4因式定理!!

因為 2x-1 是 f(x) 的因式
所以 f(1/2) = 0
k^2 (1/2)^3 + 8(1/2)^2 + (k-1)(1/2) + (1-k^2) = 0
k^2 / 8 + 2 + k/2 - 1/2 + 1 - k^2 = 0
-7/8 k^2 + k/2 + 5/2 = 0
7k^2 - 4k - 20 = 0
(7k+10)(k-2) = 0
k = 2// or -10/7 (rej.)
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f(x) = 2^2 x^3 + 8x^2 + (2-1)x + (1-2^2)
=4x^3 + 8x^2 + x - 3
長除法除2x-1 :
f(x)=(2x-1)(2x^2+5x+3)
=(2x-1)(2x+3)(x+1) //