(x - 7)(x2 + 7x + 49)
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Choose the lowest of the exponents. The GCF of x3 and x5 is x3
x2(x - 8)
In the case of a binomial in general, the only way you can factor it is by looking for common factors in each term. In other words, check whether there is a common factor (in this case) in "6x" and in "27". If there is, take this factor out.
(x+2)(x2+2x+4)
(x - 6)(x2 + 6x + 36)