Answer:
The polynomial of minimum degree is .
Step-by-step explanation:
According to the statement, we appreciate that polynomial pass through the following points:
(i) , (ii)
, (iii)
, (iv)
From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:
We proceed to expand the expression until standard form is obtained:
If we know that , then:
Then, the polynomial is:
The polynomial of minimum degree is .
