2x^3+2x^2-12x+k
= (2x^3+x^2) + (x^2+1/2x ) - (25/2x-k)
= x^2(2x+1) + 1/2x(2x+1) - 25/4[2x+(-4/25k)]
2x^3+2x^2-12x+k分解因式有一个因式（2x+1）
(-4/25k) = 1
k = -25/4