First, note that \(343=7^3.\) Then use the formula for the sum of perfect cubes:
\(a^3+b^3=(a+b)(a^2-ab+b^2).\)
Therefore,
\(x^3 + 343=x^3+7^3=(x+7)(x^2-7x+49).\)
The quadratic trinomial \(x^2-7x+49\) couldn't be factored anymore, so the expression \(x^3 + 343\) has two factors \(x+7\) and \(x^2-7x+49.\)
Answer: correct choice is A.
