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Math Help - How to solve this?

  1. #1
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    Exclamation How to solve this?

    Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
    A. –6x2 + 25x + 6
    B. 6x2 + 5x + 6
    C. 6x2 – 5x + 6
    D. 6x2 – 5x – 6
    E. 6x2 – 13x – 6

    Answer is D

    How do I solve this?





    For all [r is not equal to plus or minus 2], (r squared - 5r + 6) over (r squared - 4 = ?
    A. (r - 3) over (r + 2)
    B. (r - 2) over (r + 2)
    C. (r - 2) over (r + 3)
    D. (r + 3) over (r - 2)
    E. (r + 3) over (r + 2)

    Answer is A

    How do I solve this one as well?
    Last edited by Brazuca; July 21st 2008 at 12:18 PM.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Brazuca View Post
    Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
    A. 6x2 + 25x + 6
    B. 6x2 + 5x + 6
    C. 6x2 5x + 6
    D. 6x2 5x 6
    E. 6x2 13x 6

    Answer is D

    How do I solve this?
    Are you sure "solve" is the right word?

    You've a quantity. It is called 'x'.

    "Twice x" is 2x
    "Three less than twice x" is 2x-3

    "The quantity three times x" is 3x
    "Two more than the quantity three times x" is 3x+2

    (2x-3)(3x+2) = ???

    RIGHT AWAY, notice that this leads to +6x^2. Discard Choice A.
    Next, the constant term must be -6. Discard Choices B & C.

    You tell me how to decide between D and E.
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  3. #3
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    Thanks. The way it is worded out didn't make any sense to me...

    I still need help with my second question.
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  4. #4
    Moo
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    Hullo !

    For all [r is not equal to plus or minus 2], (r squared - 5r + 6) over (r squared - 4 = ?
    A. (r - 3) over (r + 2)
    B. (r - 2) over (r + 2)
    C. (r - 2) over (r + 3)
    D. (r + 3) over (r - 2)
    E. (r + 3) over (r + 2)

    Answer is A

    How do I solve this one as well?
    You can see something nice, it's that the denominator seems to have been reduced !

    So try to factor r-5r+6 and r-4 !

    r-4=r-2. And use identity (a-b)=(a+b)(a-b).

    r-5r+6 : factor this the way you know, completing the square, using discriminant, find an obvious root (1), etc... ^^

    And observe, be concentrated, let the mathematics get into you... hmmm I've just given you the path, now you have to walk.
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  5. #5
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    Thanks Moo after a few minutes I understood it that I had to cross out the (r-2)'s
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