The problem involves factoring the expression X^6 + 8, which is presented as a polynomial factorization challenge. The subject area pertains to algebra, specifically polynomial identities and factoring techniques.
The discussion is ongoing, with participants exploring the relationship between the terms in the expression and the formula for factoring sums of cubes. Some guidance has been provided regarding the identification of a and b, but confusion remains about the reasoning process.
Participants express uncertainty about the steps leading to the identification of a and b, indicating a need for further clarification on the underlying concepts of polynomial factorization.
Nitrate said:Homework Statement
Factor
X^6+8
Homework Equations
The answer: (x^2 + 2)(x^4 - 2x^2 + 4)
The Attempt at a Solution
I'm really not sure how to arrive at the answer. Although, I have a feeling that I have to use (a + b)(a^2 - ab + b^2) because the question looks looks similar to a^3 + b^3
Dick said:You've already got it. If a^3+b^3=x^6+8, what should a and b be?
Nitrate said:I suppose this is where I'm stuck.
a= x^2
b= 2
?
I'm still a bit confused on how we got a = x^2
Dick said:You want a^3 to equal x^6, right? You don't see why (x^2)^3=x^6?