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.

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- Dec 4th 2010, 05:31 AMrcsLong Factoring
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. - Dec 4th 2010, 06:39 AMSoroban
Hello, rcs!

Your work is absolutely correct! . . . Good work!

Quote:

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:

. .

. .

. .

. .

- Dec 4th 2010, 02:18 PMrcsthank you
thank you so much Soroban. :) i was trying to solve ... thank God you checked my work. Love Live MHF!