Final answer:
The given polynomial x⁸ + 2x³ + 1 cannot be factored further with real numbers. However, if the polynomial was x²+2x+1, a perfect square trinomial, it can be factored into the form (x+1)².
Step-by-step explanation:
The given polynomial is x⁸ + 2x³ + 1. This isn't a standard type of polynomial that can be factored using typical techniques such as factoring by grouping or factoring out the greatest common factor, as there's no common factor between the terms, nor can the polynomial be arranged into groups which have a common factor. Therefore, this polynomial cannot be factored further with real numbers.
Or, suppose if the polynomial given was a typo and actually was x²+2x+1, then this is a perfect square trinomial. A perfect square trinomial is a polynomial of the form (a²+2ab+b²), and it can be factored into the form (a+b)². So in this case, x²+2x+1 can be factored into the form (x + 1)².
Learn more about Factoring Polynomials