MathDB
Polynomial Counting

Source: 2018 AMC 12B #22

February 16, 2018
algebrapolynomialAMCAMC 12AMC 12 B2018 AMC2018 AMC 12B

Problem Statement

Consider polynomials P(x)P(x) of degree at most 33, each of whose coefficients is an element of {0,1,2,3,4,5,6,7,8,9}\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}. How many such polynomials satisfy P(1)=9P(-1) = -9?
<spanclass=latexbold>(A)</span>110<spanclass=latexbold>(B)</span>143<spanclass=latexbold>(C)</span>165<spanclass=latexbold>(D)</span>220<spanclass=latexbold>(E)</span>286<span class='latex-bold'>(A) </span> 110 \qquad <span class='latex-bold'>(B) </span> 143 \qquad <span class='latex-bold'>(C) </span> 165 \qquad <span class='latex-bold'>(D) </span> 220 \qquad <span class='latex-bold'>(E) </span> 286