# MATH TIME!

Discussion in 'User Topics' started by Mr.Lame, Jan 9, 2018.

1. ### Mr.LameRegular

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My brains dead i feel it, talk to you tomorrow , Thanks again Mark I super appreciate your help.

2. ### Mr.LameRegular

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Markkkkyyy poo @MarkFL .

x^4 − 13x^2 + 36

Last question T.T

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I think you should start paying him

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4. ### Mr.LameRegular

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I pay in respect

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5. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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Okay, first we observe that this is a quadratic in x^2.

So, we want to look for two factors of 36 whose sum is -13, and they are -4 and -9...so we have:

x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9)

Now, we see both factors are differences of squares, so we have:

x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9) = (x^2 - 2^2)(x^2 - 3^2) = (x + 2)(x - 2)(x + 3)(x - 3)

And we're done.

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6. ### Mr.LameRegular

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How the fuck did you do that so fast . You rock for real though

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7. ### Mr.LameRegular

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@MarkFL can you just be my tutor? Hahahaha

8. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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Please feel free to ask any questions here, even questions about concepts and not just actual assigned problems. I will do my best to explain.

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9. ### Mr.LameRegular

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I'm going to need this more than you'd ever know!

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10. ### Mr.LameRegular

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Hey @MarkFL I do not understand how to do this question.

11. ### Mr.LameRegular

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List the four smallest elements of the set.
{y|y = x2 − 7, x integers}

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x^2*

13. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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What's the question?

14. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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Nevermind...you posted it...

15. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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What is the smallest x^2 can be?

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Infinity? D:

17. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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That's the largest value it can approach as x gets farther and farther from zero. The smallest value x^2 can be is zero, and that's when x is zero. So, given the smallest value for x^2 is zero, then the smallest value for y will be -7 because y is defined to be x^2 - 7. And so given that y(x) = x^2 - 7, we have:

y(0) = 0^2 - 7 = -7

Next we observe that if we move one unit away from zero, to ±1, we find:

y(±1) = (±1)^2 - 7 = 1 - 7 = -6

Likewise:

y(±2) = (±2)^2 - 7 = 4 - 7 = -3

y(±3) = (±3)^2 - 7 = 9 - 7 = 2

And so the 4 smallest elements of the given set are {-7, -6, -3, 2}.

18. ### Mr.LameRegular

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You lost me T.T

19. ### MarkFLLa Villa StrangiatoStaff MemberMod Squad

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Are you familiar with parabolic curves, specifically the vertex and axis of symmetry?

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