Query about Question 2 from "PrepSwift: Factoring Quadratic Equations II" [3281]

[user15440]

https://www.gregmat.com/quizzes/quiz/prepswift-factoring-quadratic-equations-ii (Question 2)

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I factored this quadratic down to (-x+2)(x-2), which, despite being in a different order, should be the same as what’s given in the solution, (2-x)(x-2).

However, the solution lists 2, -1, 1, and -2 as the respective values for a, b, c, d. Aren’t a and b switched here? The form given in the question is (ax + b)(cx + d). (2 - x) is not in the form given in the problem. 2 is not the coefficient of x as the solution implies.

2 - 1 + 1 - 2 = 0, but shouldn’t it be -1 + 2 + 1 - 2 = -2?

Could be missing something obvious but I don’t see it.

[Kweku]

@user15440

However, the solution lists 2, -1, 1, and -2 as the respective values for a, b, c, d. Aren’t a and b switched here? The form given in the question is (ax + b)(cx + d). (2 - x) is not in the form given in the problem. 2 is not the coefficient of x as the solution implies.

Thoughi it doesn’t affect the answer, you’re right in pointing a and b are switched. @Leaderboard

@user15440

2 - 1 + 1 - 2 = 0, but shouldn’t it be -1 + 2 + 1 - 2 = -2?

-1 + 2 + 1 - 2 = 0, right?

Addition is commutative/associative so switching a and b will not change answer from 0 to -2

[Leaderboard]

Indeed, fixed.

[user15440]

Ah, was somehow getting -1 + 2 = -1 in my head while doing this. Lesson learned that studying while tired is not always the best approach. Thanks, boss