Question

The coefficient of $x^{6}$ in the polynomial (x-2)(x-4)(x-6)(x-8)...(x-12)(x-14) is:
(a) -56
(b) 56
(c) -20
(d) 32

No spam answers please! Thank you

Answer 1

There are 7 factors in the given polynomial. I.e., maximum power of x is 7.
Therefore, coefficient of x^6 is
-2 + -4 + -6 + -8 + -10 + -12 + -14 = -56