What is the factored form of 343 + x^6?

A.(7 - x)(49 + 7x + x^2)

B.(7 + x)(49 – 7x + x^2)

C.(7 - x)(49 + 7x^2 + x^4)

D. (7+ x2)(49 - 7x^2 + x^4)

Guest Mar 24, 2021

#1**0 **

first, we can rewrite x^6 as (x^2)^3, and we can also rewrite 343 as 7^3.

now, we can apply the Sum of Cubes formula.

here is the sum of cubes formula, for future reference (if needed): \(x^3+y^3 = (x+y)(x^2-xy+y^2)\)

now to apply it to the current problem.

our x in this case is x^2, and our y would be 7.

so the factored form:

\(x^6+343 = (x^2+7)(x^4-7x^2+7^2)\)

= \((x^2+7)(x^4-7x^2+49)\), which is option D.

hope this helped! please let me know if you are confused about anything i did :)

idyllic Mar 24, 2021