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Math Help - Long division method of Algebraic expressions

  1. #1
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    Long division method of Algebraic expressions

    I actually know How to divide an algebraic expression using the long division method.But this one,I have no idea how to do .
    I tried to do by rearranging the term but in vain .Someone please help me out here.

    t4 -3tq+t+5 by t-1 BY LONG DIVISION METHOD

    Thank you
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  2. #2
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    Re: Long division method of Algebraic expressions

    Quote Originally Posted by NormalKid View Post
    I actually know How to divide an algebraic expression using the long division method.But this one,I have no idea how to do .
    I tried to do by rearranging the term but in vain .Someone please help me out here.

    t4 -3tq+t+5 by t-1 BY LONG DIVISION METHOD
    what is q in the second term?
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  3. #3
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    Re: Long division method of Algebraic expressions

    3 x t x q
    3tq

    sorry,what?
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  4. #4
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    Re: Long division method of Algebraic expressions

    we can start by looking at the leading terms:

    t x ? = t4.

    clearly we need t3, so our first "go-round" is to multiply t - 1 by t3, and subtract the result from t4 - 3tq + t + 5.

    note we can re-write this as:

    t4 + 0t3 + 0t2 + (1 - 3q)t + 5.

    now (t - 1)(t3) = t4 - t3, and:

    t4 + 0t3 + 0t2 + (1 - 3q)t + 5 - (t4 - t3) = t3 + 0t2 + (1 - 3q)t + 5

    we've "reduced the degree by one".

    again, just looking at the leading terms we see we need to multiply t - 1 by t2, and subtract, so (t - 1)t2 = t3 - t2, and:

    t3 + 0t2 + (1 - 3q)t + 5 - (t3 - t2) = t2 + (1 - 3q)t + 5

    now we need to multiply t - 1 by t, and subtract: (t - 1)t = t2 - t, and:

    t2 + (1 - 3q)t + 5 - (t2 - t) = (2 - 3q)t + 5

    here, we need to multiply by 2 - 3q (this will be the "last go-round"), and (t - 1)(2 - 3q) = (2 - 3q)t - (2 - 3q). another subtraction:

    (2 - 3q)t + 5 - ((2 - 3q)t - (2 - 3q)) = 5 + (2 - 3q) = 7 - 3q.

    now, without knowing what "q" is, this is as far as we can go.

    what we've done is shown that:

    t4 - 3tq + t + 5 = (t3 + t2 + t + (2 - 3q))(t - 1) + 7 - 3q.

    the quotient is: t3 + t2 + t + (2 - 3q)

    the remainder is: 7 - 3q.
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  5. #5
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    Re: Long division method of Algebraic expressions

    can I just see the work-out?Because Its very hard for me to read and understand. And can you just explain the splitting up of -3tq?
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  6. #6
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    Re: Long division method of Algebraic expressions

    Polynomial long division is difficult at best to display using LaTeX.
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  7. #7
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    Re: Long division method of Algebraic expressions

    ok.
    Can you explain the splitting up of -3tq and why we split that?Sorry I am just a beginner.
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Long division method of Algebraic expressions

    Are you talking about where -3tq+t is written as (1-3q)t?
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  9. #9
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    Re: Long division method of Algebraic expressions

    never mind.I understood the answer.Thank you Mark and Deveno
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