You can put this solution on YOUR website! the cube root of 343 is 7.
your problem becomes:
(x^3 - 7^3)
this follows the form of (x^3 - a^3) = (x - a) * (x^2 + ax + a^2)
your factored equation is:
(x-7)(x^2+7x+49)
the following link discusses factoring of polynomials. ahttp://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm
the particular sections involved in this type of problem are:
factoring the sum of two cubes.
factoring the difference of two cubes.
you can see the excerpts from those two sections below:
the section is in the bottom 1/3 of the page from that link shown above.