Track / Stage 4 / 26 of 340 #286 of 1964

Problem 286

AMC 12 late, AIME early

Algebra Difficulty 4.5 Multiple choice

5. Given $f(x)=3 x^{2}-x+4$ , $f(g(x))=3 x^{4}+18 x^{3}+50 x^{2}+69 x+48$ .
Then, the sum of the coefficients of the integer polynomial function $g(x)$ is $(\quad$ .

Pick one

Official solution

5.A.

Let the sum of the coefficients of $g(x)$ be $s$ , then $f(g(1))=3 s^{2}-s+4=188$ .
Solving for $s$ gives $s=8$ or $s=-\frac{23}{3}$ (discard).

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.