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1977 AMC 12 Question 28

AMC12 · 1977 AMC 12

Question 28

Let $g(x)=x^5+x^4+x^3$ ${}+x^2+x+1.$ What is the remainder when the polynomial $g(x^{12})$ is divided by the polynomial $g(x)?$
  1. $6$
  2. $5-x$
  3. $4-x+x^2$
  4. $3-x+x^2-x^3$
  5. $2-x+x^2-x^3+x^4$