分解因式:2x^4-15x^3+38x^2-39x+14（要详细过程的呀.

Question

分解因式:2x^4-15x^3+38x^2-39x+14（要详细过程的呀.

Answer 1

2x^4-15x^3+38x^2-39x+14
=(2x^4-2x^3)-(13x^3-13x^2)+(25x^2-25x)-(14x-14)
=2x^3(x-1)-13x^2(x-1)+25x(x-1)-14(x-1)
=(x-1)(2x^3-13x^2+25x-14)
=(x-1)[(2x^3-2x^2)-(11x^2-11x)+(14x-14)]
=(x-1)[2x^2(x-1)-11x(x-1)+14(x-1)]
=(x-1)^2(2x^2-11x+14)
=(x-1)^2[(2x^2-4x)-(7x-14)]
=(x-1)^2[2x(x-2)-7(x-2)]
=(x-1)^2(x-2)(2x-7)