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