Question

当m,n取什么值时,x-2和x-3都能整除多项式3x立方+mx平方+nx+42

Answer 1

设还有一个因式是A

则3x^3+mx^2+nx+42=A(x-2)(x-3)

当x=2时,右边=A(2-2)*(2-3)=0,所以左边也等于0

当x=3是,右边有3-3=0,所以也是0,则左边也等于0

即x=2和3时,3x^3+mx^2+nx+42都等于0

x=2,3x^3+mx^2+nx+42 =24+4m+2n+42=0

2m+n=-33 (1)

x=3,81+9m+3n+42=0

3m+n=-41 (2)

(2)-(1)

m=-8,n=-33-2m=-17

祝你学习天天向上,加油～