CSMC 2021 Part B - Question 1, CEMC UWaterloo

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Difficulty: 5

This problem is tagged with csmc, csmc21, highschool.

(Canadian Senior Mathematics Contest 2021, Part B, Question 1, CEMC - UWaterloo)
Adapted from original statement.

a) Factor $x^2 - 4$ as the product of two linear expressions in $x$.
b) Determine the integer $k$ for which $98^2 - 4 = 100k$.
c) Determine the positive integer $n$ for which $(20 - n)(20 + n) = 391$.
d) Prove that $3999991$ is not a prime number. (do not answer)

Answer Submission Note(s)
Please do not answer the final part, it is only included for integrality. Your answer should be a product of linear expressions (with no spaces) - in the form $(x+r)(x-s)$, followed by a single integer, followed by one positive integer. All of these part answers must be space-separated.

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