Demonstrate several ways of evaluating a 10-degree polynomial. The polynomial is formed from the ten roots 1/3 8/7 2.1 3.2 4.3 5.4 6.6 7.7 8.8 9.9 and has the following floating point coefficients to machine accuracy (from low to high power, that is, from ao to a10) ao 263181.10629888007 - 1467883.5529881604 2745869.426605989 -2535885.7388542863 1348084.367903810 -444015.39169047633 93545.52310952383 - 12616.661904761906 1052.9380952380952 -49.476190476190481 1.0 a10 1a. Make a spreadsheet to evaluate the polynomial by product of linear factors, linear combination of powers, Horner's Method Be sure to set the display precision to 15 places. 1b. How many additions and how many multiplications does each of the three methods use? (Look at the spreadsheet and count how many additions and how many multiplications it must do when you put in a new x.) 1c. For each root, evaluate the polynomial by each method and report the polynomial value. Obviously the root method should give all zeroes, but is Horner's Method more accurate than the linear combination method? Demonstrate several ways of evaluating a 10-degree polynomial. The polynomial is formed from the ten roots 1/3 8/7 2.1 3.2 4.3 5.4 6.6 7.7 8.8 9.9 and has the following floating point coefficients to machine accuracy (from low to high power, that is, from ao to a10) ao 263181.10629888007 - 1467883.5529881604 2745869.426605989 -2535885.7388542863 1348084.367903810 -444015.39169047633 93545.52310952383 - 12616.661904761906 1052.9380952380952 -49.476190476190481 1.0 a10 1a. Make a spreadsheet to evaluate the polynomial by product of linear factors, linear combination of powers, Horner's Method Be sure to set the display precision to 15 places. 1b. How many additions and how many multiplications does each of the three methods use? (Look at the spreadsheet and count how many additions and how many multiplications it must do when you put in a new x.) 1c. For each root, evaluate the polynomial by each method and report the polynomial value. Obviously the root method should give all zeroes, but is Horner's Method more accurate than the linear combination method