Question

Using complete sentences, explain how you would factor completely x^9 – 64?

Answer 1

and then use
\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 2

Sorry a^3-b^3

Answer 3

well x^9 you can write as (x^3)^3 and 64 as 4^3 so it is (x^3)^3-4^3 now you can use the formula: a^3-b^3=(a-b)(a^2+ab+b^2) so it is (x^3-4)(x^6+4x^3+16) now using the same formula you can factor x^3-4 as:\[(x-\sqrt[3]{4})(x^2+\sqrt[3]{4}*x+\sqrt[3]{16})\] now x^6-4x^3+16 you can factor using the substitution x^3=t so you'll get:\[t^2+4t+16\] and you can find the solutions for this quadratic equations x1 and x2 so you can factor it like (x-x1)(x-x2) and that would be complete factorization