Question

x的四次方加2x的三次方加x的平方加1加2乘（x加x的平方）的因式分解

Answer 1

x的四次方加2x的三次方加x的平方加1加2乘（x加x的平方）
=x^4+2x^3+x^2+1+2(x+x^2)
=x^4+2x^3+x^2+1+2x+2x^2
=x^4+2x^3+3x^2+2x+1
=x^4+4x^3+6x^2+4x+1-2x^3-3x^2-1x
=(x+1)^4-2x^3-3x^2-1x
=(x+1)^4-x(2x^2+3x+1)
=(x+1)^4-x(2x+1)(x+1)
=(x+1)[(x+1)^3-x(2x+1)]
=(x+1)(x^3+3x^2+3x+1-2x^2+x)
=(x+1)(x^3+x^2+4x+1)