Question

已知f(x)=6x^4-x^3-6x^2-x-12 (1)求证:f(x)能被2x-3和3x+4整除 (2)将f(x)因式

Answer 1

证明：

f(x)=6x^4-x^3-6x^2-x-12

=6(x^4-x^2-2)-(x^3+x)

=6(x^2-2)(x^2+1)-(x^2+1)x

=(x^2+1)(6x^2-12-x)

=(x^2+1)(2x-3)(3x+4)

两个问题得证