Question 1119660
a) Find x:
x^5+ x^4+ x^3+ x^2+1=0
I have factored it : (x^2+ x+1)(x+1)(x^2-x+1)
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Then (x^2+ x+1)(x+1)(x^2-x+1) = 0
--> x = -1 is the most obvious solution
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But
f(x) = x^5+ x^4+ x^3+ x^2+1
f(-1) = -1 + 1 - 1 + 1 + 1 = 1, not zero, so (x+1) is not a factor.
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b)Factoring:
2x^2y^2+2y^2z^2+2x^2z^2-x^4-y^4-z^4