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The y5 term and the constant term have coefficient factors of 1, so try
(y-1) as one factor. Doing so yields a quotient of y4+y2+1.
Factoring this is perhaps conceptually harder. This can be recognized as
y4+y2+1 = (y4+2y2+1) - (y2) = (y2+1)2-y2 = ((y2+1) + y)((y2+1) - y)
So, the factored version of the original expression is ...
(y-1)(y2+y+1)(y2-y+1)
(y-1) as one factor. Doing so yields a quotient of y4+y2+1.
Factoring this is perhaps conceptually harder. This can be recognized as
y4+y2+1 = (y4+2y2+1) - (y2) = (y2+1)2-y2 = ((y2+1) + y)((y2+1) - y)
So, the factored version of the original expression is ...
(y-1)(y2+y+1)(y2-y+1)
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