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?
The solution to Factor X^6+8 is not a single number, but a polynomial expression in terms of X^6 and 8.
To solve Factor X^6+8, you can factor out the GCF (greatest common factor) and then use the polynomial factoring techniques such as grouping, difference of squares, and trinomial factoring.
The factors of Factor X^6+8 are (X^6+8) and 1, (X^3+2) and (X^3-2), (X^2+4) and (X^4-4X^2+16), (X+8) and (X^5-8X^4+64X^3-512X^2+4096X-32768).
Yes, Factor X^6+8 can be simplified by factoring out the GCF and then using the fundamental theorem of algebra to rewrite it as a product of linear and quadratic factors.
No, Factor X^6+8 is not a prime polynomial as it can be factored into smaller polynomials. A prime polynomial is one that cannot be factored into smaller polynomials.