Choose one of the factors of x3 + 343

If we observe closely the given, we can note that the terms given are perfect cubes. That is,

x^3 is cube of x and

343 is cube of 7

Hence, the expression is the sum of two cubes. For the sum of cubes, we follow the following rule for the factoring:

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

Applying the rule to the given, the factors would be:

X^3 + 373 = (x + 7) (x^2 - 7x + 49)