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MMLU / Suppose that f(x) is a polynomial that has degree 6 and g(x) is a…

Problem

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question

Suppose that f(x)f(x) is a polynomial that has degree 66 and g(x)g(x) is a polynomial that has degree 33. If h(x)h(x) is also a polynomial such that f(g(x))+g(h(x))+h(f(x))f(g(x)) + g(h(x)) + h(f(x)) is a polynomial of degree 3636, then what is the degree of the polynomial hh?
Plain-text mathematical notation (without MathML)
Suppose that f(x) is a polynomial that has degree 6 and g(x) is a polynomial that has degree 3. If h(x) is also a polynomial such that f(g(x))+g(h(x))+h(f(x)) is a polynomial of degree 36, then what is the degree of the polynomial h?
Original LaTeX notation
Suppose that $f(x)$ is a polynomial that has degree $6$ and $g(x)$ is a polynomial that has degree $3$. If $h(x)$ is also a polynomial such that $f(g(x)) + g(h(x)) + h(f(x))$ is a polynomial of degree $36$, then what is the degree of the polynomial $h$?

choices

  1. 72
  2. 6
  3. 18
  4. 12

subject

high_school_mathematics

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Source and history

task_id
63952b5f-595f-5488-b26b-ac6e93e4a446
task_key
all--test--63952b5f-595f-5488-b26b-ac6e93e4a446
task_revision_id
1
config / split
all / test

Official source

initial import