Complete the table of ordinary differences from these data: 1.20 1.25 1.30 0.1823 0.2231 0.2624 1.35 1.40 1.45 1.50 0.3001 0.3365 0.3716 0.4055 a. what degree of polynomial is required to exactly fit all seven points to within three significant digits? b. what polynomial of lesser degree will almost fit to the same precision? c. justify your answer to part (b).