A1. How many polynomials of degree 5, whose all coefficients are equal to 1 or -1, have a root at 1?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 24
A1. The value of the polynomial at the point 1 is equal to the sum of all the coefficients of the polynomial. Since this value must be equal to 0, exactly three coefficients must be equal to 1, and three must be equal to -1. The number of sought polynomials is thus $\binom{6}{3}=20$.