Given any "n" values, there exist a unique polynomial of degree n-1 or less that gives those values. Here you are given 4 values so there exist a unique polynomial of degree 3 or less such, which we can write as z=ai3+bi2+ci+d. The four given values give four equations to solve for a, b, c, and d:
216a+ 36b+ 6c+ d= 7
343a+ 49b+ 7c+ d= 5
512a+ 64b+ 8c+ d= 3
729a+ 81b+ 9a+ d= 1
Of course, here that's overkill. Solving those equations we quickly find that a and b are 0.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.