factoring question?

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How do you factor out 1+x+x^2+x^3+x^4+x^5 using only polynomials with integer coefficients?

2006-12-12 09:31:49 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

can you plz explain how you did it?

2006-12-12 09:44:16 · update #1

3 answers

(x + 1) (x^2 + x + 1) (x^2 - x + 1)

By group factorization:

(x^5 + x^4) + (x^3 + x^2) + (x + 1)

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

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

then the first part factored gives us
(x^2 + x + 1) (x^2 - x + 1) (x + 1)

2006-12-12 09:38:56 · answer #1 · answered by Math-Chem-Physics Teacher 3 · 0⤊ 0⤋

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

2006-12-12 09:34:19 · answer #2 · answered by Minnesota_Slinger 3 · 0⤊ 0⤋

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

2006-12-12 09:35:31 · answer #3 · answered by raj 7 · 0⤊ 0⤋