Question 5
Find all polynomials $P(x)$ with integer coefficients such that
$$Q(x)=(x^2+6x+10)P(x)^2-1$$
is the square of a polynomial with integer coefficients.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; this rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.
$$Q(x)=(x^2+6x+10)P(x)^2-1$$
is the square of a polynomial with integer coefficients.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; this rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.