Question

The sum of all the coefficients of the polynomial
(x-2)^6 (x-4)^2 +(x+1)^3 (x-2)^3 + (x+1)^2 (x-4)^3​

Answer 1

Step-by-step explanation:

To find the sum of the coefficients,we substitute x with 1

i.e. we find the value of p(1)

(x-2)^6 (x-4)^2 +(x+1)^3 (x-2)^3 + (x+1)^2 (x-4)^3

=(1-2)^6 * (1-4)^2 + (1+1)^3 * (1-2)^3 + (1+1)^2 * (1-4)^3

=(-1)^6 * (-3)^2 + (2)^3 * (-1)^3 + (2)^2

* (-3)^3

=(1)(9) + (8)(-1) + (4)(-27)

=9 + (-8) + (-108)

=9 - 8 - 108

=-107