x^4 + 2x^3 + 3x^2 + 2x + 1
x ^4 + x^2 + 2x^3 + 2x^2 + 2x + 1
(x^4 + 2x^3 + x^2) +( 2x^2 + 2x +1)
x^2 ( x^2 + 2x + 1) + 2 (x^2 + x) + 1
x^2(x+1)^2 + 2x (x+1) + 1
[x(x+1)+ 1]^2 + 2[x(x+1)] + 1
[x(x+1) + 1]^2
(x^2 + x + 1)^2 answer.
Hello, rcs!
Your work is absolutely correct! . . . Good work!
The coefficients reminded me of an arithmetical phenomenon:
. . .
So I immediately concluded that we have: .
Already knowing the answer, it was easy to demonstrate the factoring:
. .
. .
. .
. .