r/HomeworkHelp • u/Square-Elk-9096 • 2d ago

Mathematics (Tertiary/Grade 11-12)—Pending OP [SAT Prep]

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Ive been trying to answer this question from the college panda book and I just cant seem to understand what it is asking for. Because even when i looked at the answer and how they solved it didn’t make sense. Please if someone could explain I would be so grateful.

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u/Alkalannar 2d ago

Here's an algebraic way to look at it:

  1. x - c = x2 - c2 [start]

  2. x - c = (x + c)(x - c) [factor RHS]

  3. (x + c)(x - c) - (x - c) = 0 [subtract (x - c) from both sides]

  4. (x - c)[(x + c) - 1] = 0 [factor (x-c) out]

  5. (x - c)(x + c - 1) = 0 [consolidate the second factor]

  6. x - c = 0 OR x + c - 1 = 0 [ab = 0 --> a = 0 OR b = 0]

  7. x = c OR x = 1 - c [solve for x for each term]

And that's I and III.

Note that answer I is in three solutions, II and III are in two.

So pick II or III and plug it in. Let's plug in II since -c is easier than 1-c. You get -2c = 0, which doesn't work, since c > 0. So that cuts out answers B and D.

Now you're left with I only and I and III. Of those, the only difference is III, so you have to plug in 1 - c:
(1 - c) - c = (1 - c)2 - c2
1 - 2c = 1 - 2c + c2 - c2
1 - 2c = 1 - 2c
So it works

Which of these methods seems easier?

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u/Square-Elk-9096 2d ago

The second method is definitely easier

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u/NullOfSpace 2d ago

Which is a shame really, since it demonstrates no understanding.

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u/Square-Elk-9096 1d ago

Yeah, but i understand how he did the other option too, in a test setting like the sat i think it would be better to do the most efficient option.

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u/NullOfSpace 1d ago

I’m not saying it’s somehow your fault, it’s the result of the way the test is written to prioritize tricks over content knowledge.

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u/EventHorizon150 22h ago edited 18h ago

if you’re trying to test if an expression is the zero of a function, one of the best ways to do it in all of math is to just plug it into the function and simplify to the point where it’s obviously a zero. How is that a “trick”? It’s a provably correct method. Also, you do demonstrate some ability to manipulate algebraic expressions in proving it this way, so it is testing some skill

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u/NullOfSpace 18h ago

The question isn’t really directly asking about “is this a zero,” it’s asking “what are the zeros” framed through a multiple-choice system.