37763a18-ring-strategy-is-most-efficient-for-x4-16-and-what-is-the-complete-fact

Question

Which factoring strategy is most efficient for x4−$$16x^4 - 16$$, and what is the complete factorization?

Accepted Answer

Use the difference of squares twice;x4−16=(x−$$2)(x+2)(x2+4)x^4 - 16 = (x - 2)(x$$ + $$2)(x^2 + 4)$$

Answer

No factorization is possible over the reals;x4−$$16x^4-16$$

Answer

Factor by grouping into (x4−x2)+(x2−$$16)(x^4$$ - $$x^2$$) + $$(x^2 - 16$$); 2x2(x2−$$8)2x^2$(x^2-8) $$

Answer

Extract the GCF $$x2x^2$$ first; (x−$$2)(x+2)(x2+4)(x-2)(x+2)(x^2+4)$$

Which factoring strategy is most efficient for x4−16x^4 - 16, and what is the complete factorization?