Final answer:
The student needs to find two polynomials that add up to 16n^3 + 13n^2 + Zn - 10. One possible solution is P1(n) = 8n^3 + 5n^2 + Z/2 n - 5 and P2(n) = 8n^3 + 8n^2 + Z/2 n - 5, which when added, result in the given polynomial.
Step-by-step explanation:
The student is tasked with selecting two polynomials whose sum equals 16n^3 + 13n^2 + Zn - 10. Although the variable Z is typically not used in polynomials and could be a typo for another variable such as z, the general approach to this problem remains the same: find two polynomials that when added together, their respective terms of the same degree combine to give the terms of the given polynomial.
An example solution could be finding two polynomials P1(n) and P2(n) such that the sum P1(n) + P2(n) yields the target polynomial. To solve this, assume P1(n) and P2(n) have terms whose degrees match those in the given polynomial. Their coefficients should add up to the coefficients of 16n^3, 13n^2, Zn, and -10 respectively. Here's an illustrative pair of polynomials that could act as a possible solution:
- P1(n) = 8n^3 + 5n^2 + Z/2 n - 5
- P2(n) = 8n^3 + 8n^2 + Z/2 n - 5
When P1(n) and P2(n) are added together, each corresponding term of the same degree adds up to give the target polynomial's terms.