Question

用两种不同的分组分解法分解因式x^4+x^3+2x+x+1

Answer 1

x^4+x^3+2x+x+1

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

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

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

x^4+x^3+2x+x+1

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

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

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