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Math Help - polynomial

  1. #1
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    Post polynomial

    Need help with Factoring a polynomial please.
    3x^2+7x+2, my answer (3x+1)(2x+1) but I'm not sure it could be (3x+1)(x+2). thanks for taking time to look it over.
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  2. #2
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    Quote Originally Posted by wayne View Post
    Need help with Factoring a polynomial please.
    3x^2+7x+2, my answer (3x+1)(2x+1) but I'm not sure it could be (3x+1)(x+2). thanks for taking time to look it over.
    Hello,

    use completing the square to factor this sum:

    3x^2+7x+2 = 3\left(x^2 + \frac{7}{3}x+\frac{2}{3}  \right) = 3\left( \left(x^2 + \frac{7}{3}x+\frac{49}{36}\right) - \frac{49}{36} +\frac{2}{3}  \right) = 3\left( \left(x + \frac{7}{6}\right)^2 - \frac{25}{36} \right) = 3\left( \left(x + \frac{7}{6}\right)^2 - \left(\frac{5}{6} \right)^2 \right)

    As you can see you've got a difference of squares which can be factored easily:

    3\left( \left(x + \frac{7}{6}\right)^2 - \left(\frac{5}{6} \right)^2 \right) = 3\left( x + \frac{7}{6}+ \frac{5}{6} \right) \left( x + \frac{7}{6} - \frac{5}{6}  \right)

    Collect the fractions and multiply the 2nd bracket by the factor 3:

    (x+2)(3x+1)

    A personal remark: I know there exist formulae which will give you the result directly and immediately. But they use the way I've demonstrated too - you only can't see it at once.
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  3. #3
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    thanks

    What I thought first was right, thanks for checking.
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  4. #4
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    thanks

    What I thought first was wrong, thanks for checking.
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