Question

If the coefficients and the constants of any polynomial add up to zero, the polynomial is divisible by (x-1)

True or False

Answer 1

consider the polynomial : \[P(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0\]

Answer 2

plugin x = 1 and notice that you get sum of coefficients and constant term on the right hand side

Answer 3

next appeal to remainder/factor theorem

Answer 4

mhmm