x⁴-3x³-15x²+19x+30=0

X=5

x4-3x3-15x2+19x+30=x4-4x3+4x2+x3-4x2+4x-15x2+15x+30=x2(x-2)2+x(x-2)2-15(x-2)(x+1)
=(x-2)(x3-2x2+x2-2x-15x-15)=(x-2)(x3+x2-2x2-2x-15x-15)=(x-2)(x+1)(x2-2x-15)
=(x-2)(x+1)(x-5)(x+3)=0
x1=-3
x2=-1
x3=2
x4=5

f(x)=x⁴-3x³-15x²+19x+30 ; 30有因数1,2,3,5....,-1,-2,-3,...
f(-1)=0 ; f(2)=0 ;f(-3)=0;f(5)=0
=>(x+3)(x+1)(x-2)(x-5)=0∴x=-3 or x=-1 or x=2 or x=5

可以化简成
(x+3)(x+1)(x-2)(x-5)=0
∴x=-3 or x=-1 or x=2 or x=5

x⁴-3x³-15x²+19x+30=0
x⁴+x³-4x³-4x²-11x²-11x+30x+30=0
x³(x+1)-4x²(x+1)-11x(x+1)+30(x+1)=0
(x+1)(x³-4x²-11x+30)=0
(x+1)(x³-2x²-2x²+4x-15x+30)=0
(x+1)[x²(x-2)-2x(x-2)-15(x-2)]=0
(x+1)(x-2)(x²-2x-15)=0
(x+1)(x-2)(x-5)(x+3)=0
∴x=-3,-1,2,或5