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Math Help - Quadratic Functions

  1. #1
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    Quadratic Functions

    Ok guys, sorry if im posting this in the wrong section; dont know where quadratics belong.

    Anyway, so I have a maths test next week, and my maths teacher handed out practice tests (from years back) for us to get a look at what we're dealing with. Anyway, im going pretty well with it, except theres 1 question im stuck at. Could you please help me do it?

    Question: Factorize each of the following expressions, over R if necessary.

    1) 16x^2-81
    2) x^2+4x-5
    3) -7(x-3)^2+63
    4) 2x^2-22x+8
    5) 7(9+5)^2 -6(9+5)-1

    Thanks
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by mcaelli View Post
    Ok guys, sorry if im posting this in the wrong section; dont know where quadratics belong.

    Anyway, so I have a maths test next week, and my maths teacher handed out practice tests (from years back) for us to get a look at what we're dealing with. Anyway, im going pretty well with it, except theres 1 question im stuck at. Could you please help me do it?

    Question: Factorize each of the following expressions, over R if necessary.

    1) 16x^2-81
    2) x^2+4x-5
    3) -7(x-3)^2+63
    4) 2x^2-22x+8
    5) 7(9+5)^2 -6(9+5)-1

    Thanks
    Hi mcaelli,
    1) 16x^2-81

    This is the classic difference of two squares. Use the following model to factor:

    a^2-b^2=(a-b)(a+b)

    2) x^2+4x-5

    For this one, think of two numbers whose product is -5 and whose sum is 4. You'll discover that there is only one solution to that question: 5 and -1

    (x+5)(x-1)

    3) -7(x-3)^2+63

    Try expanding everything and collecting terms to get a neat quadratic expression. Then, we'll try to factor it. Or, better still, do what stapel suggests in her post. It's cleaner.

    4) 2x^2-22x+8

    Observe that the expression has a common monomial factor.

    2(x^2-11x+4)

    5) 7(9+5)^2 -6(9+5)-1

    This is a strange little booger!

    Let x = (9+5), then 7x^2-6x-1

    (7x+1)(x-1)

    Now back substitute to get [7(9+5)+1)][(9+5)-1]

    I really don't know what you might want to do next since everything here is numbers.
    Last edited by masters; April 18th 2009 at 07:19 AM.
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  3. #3
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    Quote Originally Posted by mcaelli View Post
    Factorize each of the following expressions....

    1) 16x^2-81
    To learn how to factor a difference of squares, try here.

    Quote Originally Posted by mcaelli View Post
    2) x^2+4x-5
    To learn how to factor regular quadratics, try here.

    Quote Originally Posted by mcaelli View Post
    3) -7(x-3)^2+63
    To learn how to take the common factor out front, try here. This will leave you with:

    . . . . . -7\left((x\, -\, 3)^2\, -\, 9\right)[/quote]

    Then factor the remaining difference of squares.

    Quote Originally Posted by mcaelli View Post
    4) 2x^2-22x+8
    Take the common factor of "2" out front. What remains does not factor "over the integers". However, you are supposed to plow on regardless. So work backwards from the zeroes:

    Set the quadratic equal to zero, plug it into the Quadratic Formula, and find the roots, being some (messy) numbers "a" and "b".

    Then note that "x^2 - 11x + 4 = 0 for x = a, x = b" means that "(x - a)(x - b) = 0", so the factors must be (x - a) and (x - b).

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  4. #4
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    Sweet guys, thanks alot. Still a bit unsure about Q5 but got 1-4 done so im pretty happy with it .
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by mcaelli View Post
    Sweet guys, thanks alot. Still a bit unsure about Q5 but got 1-4 done so im pretty happy with it .
    Yeah, #5 was a bit strange, I agree. But I factored it as requested. Notice the substitution I made to make it easier. This one is just arithmetic, but the instructions were to factor. That's why I left it in that form.

    Good Luck. Glad we could help.
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