早教吧 育儿知识 作业答案 考试题库 百科 知识分享

多项式的分解因式已知f(x)=2x^5-10X^4+16X^3-16X^2+14X-6,请问数学高手怎么把它分解为不可约式f(x)=2(X-1)^2(X-3)(X^2+1).

题目详情
多项式的分解因式
已知f(x)=2x^5-10X^4+16X^3-16X^2+14X-6,请问数学高手怎么把它分解为不可约式f(x)=2(X-1)^2(X-3)(X^2+1).
▼优质解答
答案和解析
f(x)=2x^5-10X^4+16X^3-16X^2+14X-6
=2x^5-2x^4-8x^4+8x^3+8x^3-8x^2-8x^2+8x+6x-6
=2x^4(x-1)-8x^3(x-1)+8x^2(x-1)-8x(x-1)+6(x-1)
=(2x^4-8x^3+8x^2-8x+6)(x-1)
=(2x^4-2x^3-6x^3+6x^2+2x^2-2x-6x+6)(x-1)
=[2x^3(x-1)-6x^2(x-1)+2x(x-1)-6(x-1)](x-1)
=(2x^3-6x^2+2x-6)(x-1)(x-1)
=[2x^2(x-3)+2(x-3)](x-1)(x-1)
=2(x^2+1)(x-3)(x-1)(x-1)