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Math Help - Finding LCM of polynomials? (factoring)

  1. #1
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    Finding LCM of polynomials? (factoring)

    Ok, I know how to do everything in this problem EXCEPT the factoring. I'm very weak in factoring and I only know how to do the ones with obvious answers. This problem has been frustrating me for a long time, and I need to do it tonight. There is a test tomorrow, and I don't know how to do it. I'm sort of freaking out. Hopefully you can help me!!

    "Find the least common multiple of each pair or polynomials."

    4x^2 + 12x +9 and 4x^2 - 9
    My first thought was that I could factor out the 4, but quickly decided it wouldn't work because of the 9. How do I factor these?? Please help!
    Last edited by A dumb person; April 2nd 2009 at 07:44 PM.
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  2. #2
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    Quote Originally Posted by A dumb person View Post
    Ok, I know how to do everything in this problem EXCEPT the factoring. I'm very weak in factoring and I only know how to do the ones with obvious answers. This problem has been frustrating me for a long time, and I need to do it tonight. There is a test tomorrow, and I don't know how to do it. I'm sort of freaking out. Hopefully you can help me!!

    My first thought was that I could factor out the 4, but quickly decided it wouldn't work because of the 9. How do I factor these?? Please help!
    1. I assume that you know

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

    2. If you didn't see that the first term is a complete square you have to factor it the long way. You suggested to factor out the 4 ... This way is possible:

    4x^2+12x+9=4\left(x^2+3x+\frac94\right)

    Complete the square:

    4\left(x^2+3x+\frac94\right) = 4\left(x^2+3x{\color{blue}+\left(\frac32  \right)^2 - \left(\frac32  \right)^2} + \frac94\right)

    4\left(x^2+3x{\color{blue}+\left(\frac32  \right)^2 - \left(\frac32  \right)^2} + \frac94\right) = 4\left(x+\frac32\right)^2 = (2x+3)^2

    3. Now you have the terms factored:

    \begin{array}{lcr}4x^2+12x+9& = &(2x+3)(2x+3) \\ 4x^2-9& =& (2x-3)(2x+3)\end{array}

    4. I'll leave the rest for you.
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  3. #3
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    Quote Originally Posted by A dumb person View Post
    How do I factor these?
    I suspect that you're being expected to recognize the pattern for differences of squares and for perfect-square trinomials.

    . . . . . a^2\, -\, b^2\, =\, (a\, +\, b)(a\, -\, b)

    . . . . . a^2 x^2\, \pm\, 2abx\, +\, b^2\, =\, (ax\, \pm \,b)^2

    Memorize these patterns before the test!
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