Question

已知-6x^3+ax^2+8x+b=(x+1)(mx+1)(3x+n),求a,b,m,n的值

Answer 1

(x+1)(mx+1)(3x+n)

=[mx^2+(m+1)x+1](3x+n)

=3mx^3+[mn+3(m+1)]x^2+[n(m+1)+3]x+n=-6x^3+ax^2+8x+b

所以：3m=-6,m=-2

nm+n+3=8 n=-5

[mn+3(m+1)]=a,-2n-3=a,a=7

b=n=-5

a=7,b=-5,m=-2,n=-5