1979 AHSME Problems/Problem 25
Problem 25
If and are the quotient and remainder, respectively, when the polynomial is divided by , and if and are the quotient and remainder, respectively, when is divided by , then equals
Solution
Solution by e_power_pi_times_i
First, we divide by using synthetic division or some other method. The quotient is , and the remainder is . Then we plug the solution to into the quotient to find the remainder. Notice that every term in the quotient, when , evaluates to . Thus .
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.