Question

Choose one of the factors of x^3 + 343.
Answer
A. None of the above
B. x^2 + 7x + 49
C. x – 7
D. x^2 – 14x + 49

Answer 1

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.