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

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

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

=x³(x+1)+x²(x+1)+x(x+1)+(x+1)
=(x+1)(x³+x²+x+1)
=(x+1)【x²(x+1)+(x+1)】
=(x+1)²(x²+1)

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