待定系数法因式分解

令x⁴-2x³-27x²-44x+7=(x²+ax+b)(x²+cx+d)
x⁴-2x³-27x²-44x+7
=(x²+ax+b)(x²+cx+d)
=x⁴+(a+c)x³+(ac+b+d)x²+(ad+bc)x+bd
a+c=-2
ac+b+d=-27
ad+bc=-44
bd=7
解得a=-7 b=1 c=5 d=7
x⁴-2x³-27x²-44x+7=(x²-7x+1)(x²+5x+7)