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)