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Math Help - factoring

  1. #1
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    factoring

    Can someone help me understand how to factor these questions? I mean work out one of them step by step so, I can try to figure one out. Thanks a bunch!
    1. Factor completely.
    2x2 + 40x + 200
    a) 2(x + 10)(x + 20)
    b) 2(x + 20)2
    c) (2x + 10)2
    d) 2(x + 10)2
    e) none of the above

    2. Factor 4x2 - 20x + 25. Select the answer.
    a) 2x-5
    b) (2x-5)2
    c) (2x+5)2
    d) 2x+5
    e) none of these
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by starrynight View Post
    1. Factor completely.
    2x2 + 40x + 200
    a) 2(x + 10)(x + 20)
    b) 2(x + 20)2
    c) (2x + 10)2
    d) 2(x + 10)2
    e) none of the above
    Well even if you can't manage to factor them you can multiply each of the answers out to see which one is correct.

    2x^2 + 40x + 200

    First note that there is a common factor of 2 in each term:
    2x^2 + 40x + 200 = 2(x^2 + 20x + 100)
    (so you should know automatically that c) can't be correct, right?)

    Now let's take a look at x^2 + 20x + 100.

    Take the leading coefficient (1) and multiply it by the constant term (100), in this case giving us 100.

    Now list all possible pairs of factors of 100:
    1, 100
    2, 50
    4, 25
    5, 20
    10, 10
    20, 5
    25, 4
    50, 2
    100, 1
    (and we have all the negatives as well: -1, 100 etc.)

    Now find out which of these pairs add up to be the linear coefficient (20). I get that 10 + 10 = 20.

    So what you want to do is to write 20x = 10x + 10x in your quadratic. So we get
    2x^2 + 40x + 200 = 2(x^2 + 20x + 100)

    = 2(x^2 + 10x + 10x + 100)

    = 2([x^2 + 10x] + [10x + 100])

    = 2(x[x + 10] + 10[x + 10])

    = 2(x + 10)(x + 10) = 2(x + 10)^2

    Try this approach on your second problem.

    -Dan
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  3. #3
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    Thanks for your help!
    I think the answer is none of the above. Am I right?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by starrynight View Post
    Thanks for your help!
    I think the answer is none of the above. Am I right?
    As I said before you can find the correct answer simply by FOILing out each possible answer, so there should be no doubt in your mind.

    No, you don't have it correct.
    4x^2 - 20x + 25

    Using the same method as I posted earlier:
    4 times 25 = 100

    Factors of 100:
    1, 100
    2, 50
    etc.

    And as I said, don't forget about the double negative pairs like -2, -50 etc.

    I get that -20 = -10 + -10, so put the quadratic in the form:
    4x^2 - 20x + 25 = 4x^2 - 10x - 10x + 25

    = (4x^2 - 10x) + (-10x + 25)

    and do your factoring from there.

    -Dan
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