Question

分解因数：x的四次方-4x+3急

Answer 1

x^4-4x+3

=x^4-1-4x+4

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

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

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

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

=(x-1)[(x^3-1)+(x^2-1)+(x-1)]

=(x-1)[(x-1)(x^2+x+1)+(x-1)(x+1)+(x-1)]

=(x-1)^2[(x^2+x+1)+(x+1)+1]

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