Choose any polynomial of degree 1 and do the comparison using the table example below. Pick c any number you wish. Then do the same with any polynomial of degree 2, 3, and 4.
Then do the same with a polynomial of degree 5 (or 6), 7 (or 8), and 9 (or 10). Then look at
the pattern and generalize it with a polynomial of degree n.
Polynomial
f(1) = x+1
f(x) = x + 3x + 2
Calculation Performance
Normal Substitution Synthetic Division
1
5
4
Substitution or
Synthetic Wins?
Substitution
Synthetic
Does this generalization change if the coefficient is 1 for all the variables in all the
polynomials? If you've already picked the coefficients to be 1 in all the variables, then does
the generalization change if the coefficients are selected different from 1? Do the table
again and check for all the polynomials.
After doing the analysis above, write a recommendation for calculator/computer
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acer