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

correct choice is A.

Explanation:

Answer 2

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.