f(x)=ax^3-13x^2+bx-60除以3x^2-14x-5时,余式是7x-35,求a和b.
问题描述：
f(x)=ax^3-13x^2+bx-60除以3x^2-14x-5时,余式是7x-35,求a和b.
答
该体为待定系数,设原式=(3x^2-14x-5)(cx加d)=3cx^3加(3d-14c)x^2加(-14d-5c)x-5d则对应项相等,-5d=-60-(-35);3d-14=-13解得c=2;d=5则a=3c=6;b=7-14d-5c=-73