If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?

a^3 – 3a^2b + 3ab^2 – b^3
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(a – b )(a – b)

If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?

Here’s a question from the May 2023 (US) SAT, non-calculator section

Here’s a question from the May 2023 (US) SAT, non-calculator section:

Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by 10% of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?

A) 50
B) 42
C) 39
D) 35

I know we can solve this by subtracting 10% of the current value 5 times, but is there a more direct way to solve, maybe as a function?

Hi Mike, Can you explain this Q #29 from Calculator section of Oct 2022 PSAT?

Hi Mike,
Can you explain this Q #29 from Calculator section of Oct 2022 PSAT:

A quadratic function can be used to model the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. Based on the model, what was the height, in feet, of the object 1 second after it was launched?