To write a polynomial function, it is essential to know its degree, where the degree is the number of terms or coefficients for the polynomial minus 1. In this case, we have 4 coefficients: 7, 21, 14, and 8, which necessitate the construction of a polynomial of degree 3 plus an additional term to equal a total of 5 terms.
For simplicity, let's denote the variable of the polynomial expression as 'x'. Now, let's organize the coefficients and corresponding exponents of the 'x' variable.
First, you assign the coefficient '7' to the term with the variable 'x' raised to the power '0'. This will give us the term '7*x^0'. The 'x^0' just equals 1, so this term is equivalent to 7*1 or just 7.
Second, the coefficient '21' shall be assigned to the term with the variable 'x' raised to the power '1'. So, the second term becomes '21*x^1'. Since 'x^1' is just 'x', this term simply becomes 21x.
Thirdly, correlate the coefficient '14' to the term with the variable 'x' raised to the power '2', giving us '14*x^2'.
The fourth coefficient '8' is associated with the term with the variable 'x' raised to the power '3', yielding the term '8*x^3'.
Finally, to obtain a total of five terms, we add an extra term without an explicit coefficient but with 'x' raised to the power equal to the total number of terms (here 4). This term becomes 'x^4'. Since the coefficient for this term is not explicitly defined, it is implicitly understood to be 1 (based on the rules of algebra).
So, when you put all these terms together, the polynomial expression you get is:
'7*x^0 + 21*x^1 + 14*x^2 + 8*x^3 + x^4'
Simplifying this expression by removing the trivial power terms ('x^0' and 'x^1'), the function simplifies to a more straightforward expression:
'7 + 21*x + 14*x^2 + 8*x^3 + x^4'
This is the final five-term polynomial expression with the assigned coefficients.