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Thread: How do you solve this division

  1. #1
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    Ontario Canada
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    How do you solve this division

    (16a^3-17a+10)/ (4a+5)

    I have to solve this operation. I should have a quotient and remainder??


    How do I solve this?
    Thanks
    Joanne
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  2. #2
    Senior Member
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    $\displaystyle
    16 a^3 -17a+10 = (4a+5)(something)
    $

    In order to get a term on the left like $\displaystyle
    16 a^3
    $ the $\displaystyle 4a$ has to multiply $\displaystyle 4a^2$, so let's try:

    $\displaystyle
    16 a^3 -17a+10 = (4a+5)(4a^2+something)
    $

    Unfortunately now the right hand side (RHS) is:
    $\displaystyle
    16 a^3 +20a^2+something
    $

    We don't want the $\displaystyle
    20a^2 $. So let's modify the 'something'. We have to multiply the $\displaystyle 4a$ by $\displaystyle -5a$ to get a $\displaystyle -20a^2$.

    So the equation is now

    $\displaystyle
    16 a^3 -17a+10 = (4a+5)(4a^2-5a+something)
    $

    We've added an $\displaystyle a^2$ term and an $\displaystyle a$ term. The last term to add is a constant term.

    Can you find the last constant in the right hand side? Whatever is left over is the remainder in your division.
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