x² -2x=5
x²-2x-5=0
x四次方+3x³-12x² -31x-15
=x的4次方-2x³-5x²+5x³-10x²-25x+3x²-6x-15
=x²(x²-2x-5)-5x(x²-2x-5)+3(x²-2x-5)
=(x²-2x-5)(x²-5x+3)
∵x²-2x-5=0
∴原式=0