Answer:
66
Explanation:
You want the remainder from (x^10 +2x^9 +3x^8 +...+10x +11)/(x -1).
Remainder
The remainder from dividing polynomial f(x) by (x-a) is the value f(a). Here, that means we can find the remainder by evaluating (x^10 +2x^9 +3x^8 +...+10x +11) for x=1. When we do that, we see the value is simply the sum of the coefficients:
f(1) = (1 + 2 + 3 + ... + 10 + 11) = (11)(11 +1)/2 = 66
The remainder from dividing by (x-1) is 66.
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Additional comment
The sum of integers 1..n is (n)(n+1)/2.