
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let  $P\left(X\right)=X^5+3X^4-4X^3-X^2-3X+4$ . Determine the number of monic polynomials  $Q\left(x\right)$  with integer coefficients such that  $\frac{P\left(X\right)}{Q\left(X\right)}$  is a polynomial with integer coefficients. Note: a monic polynomial is one with leading coefficient  $1$  (so  $x^3-4x+5$  is one but not  $5x^3-4x^2+1$  or  $x^2+3x^3$ ).

*2016 CCA Math Bonanza Individual #9*

Present the answer in LaTex format: \boxed{Your answer}
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