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Math Help - Quotient

  1. #1
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    Quotient

    Q)  <br />
\frac{6a^2+5a-6}{3a-2}<br />
    Q) \frac{5b^3+7b^2+12}{b+2}

    Please answer the following in steps..
    Thank you
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  2. #2
    Senior Member topher0805's Avatar
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    Quote Originally Posted by mj.alawami View Post
    Q)  <br />
\frac{6a^2+5a-6}{3a-2}<br />
    Q) \frac{5b^3+7b^2+12}{b+2}

    Please answer the following in steps..
    Thank you
    To simplify, start by factoring the numerator:

    6a^2+5a-6 = (3a-2)(2a+3)

    Which gives us:

    \frac{(3a-2)(2a+3)}{(3a-2)}

    Cancel out the common term:

    2a+3

    --------------------------------------------------------

    For the 2nd question, you can use long division. I'm not sure about the LaTeX, but it works the same as long division with integers.

    If you need to see it, this is a good tutorial: http://www.purplemath.com/modules/polydiv2.htm
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  3. #3
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    Hello, mj.alawami!

    Just factor and reduce . . .


     \frac{6a^2+5a-6}{3a-2}

    Factor: . \frac{(2a+3)(3a-2)}{3a-2}

    . . and reduce: . \frac{(2a+3)({\color{red}\rlap{//////}}3a-2)}{{\color{red}\rlap{//////}}3a-2} \;=\;2a+3



    \frac{5b^3+7b^2+12}{b+2}

    Factor: . \frac{(b+2)(5b^2-3b+6)}{b+2}

    . . and reduce: . \frac{({\color{red}\rlap{////}}b+2)(5b^2-3b+6)}{{\color{red}\rlap{////}}b+2} \;=\;5b^2-3b+6

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  4. #4
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    Quote Originally Posted by topher0805 View Post
    To simplify, start by factoring the numerator:

    6a^2+5a-6 = (3a-2)(2a+3)

    Which gives us:

    \frac{(3a-2)(2a+3)}{(3a-2)}

    Cancel out the common term:

    2a+3

    --------------------------------------------------------

    For the 2nd question, you can use long division. I'm not sure about the LaTeX, but it works the same as long division with integers.

    If you need to see it, this is a good tutorial: Polynomial Long Division

    The long division is very hard and i am getting confused in doing the second one so please tell me how to do it using the long division
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, mj.alawami!

    Just factor and reduce . . .



    Factor: . \frac{(2a+3)(3a-2)}{3a-2}

    . . and reduce: . \frac{(2a+3)({\color{red}\rlap{//////}}3a-2)}{{\color{red}\rlap{//////}}3a-2} \;=\;2a+3




    Factor: . \frac{(b+2)(5b^2-3b+6)}{b+2}

    . . and reduce: . \frac{({\color{red}\rlap{////}}b+2)(5b^2-3b+6)}{{\color{red}\rlap{////}}b+2} \;=\;5b^2-3b+6

    How did you factorise so easily the second one ?
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  6. #6
    Senior Member topher0805's Avatar
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    Quote Originally Posted by mj.alawami View Post
    How did you factorise so easily the second one ?
    He did it using long division.
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  7. #7
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    Quote Originally Posted by topher0805 View Post
    He did it using long division.
    Please show me the steps because i am desperate, i can't figure out what to do in the middle of the division

    Sorry i got it?
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