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 26 | |
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