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x³+7x²+1x+7
We factor x² out of the first two terms
We factor +1 out of the last two terms
x²(x+7)+1(x+7)
Now there are only 2 terms.
We notice that (x+7) is a common factor of both
those terms, so we factor out (x+7)
(x+7)(x²+1)
Edwin