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Math Help - Algebraic Division

  1. #1
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    Algebraic Division

    I hope this is in the correct section(i am in college and this is algebra..)

    I know this should be simple but I really can't spot where I'm going wrong.

    x^3+x^2+5x-2 is divisible by (x-2) I'm trying to completely factorise this by dividing this and then factorising the product. (this is the method i have to use for my C2 exam)

    Could someone show me the step through of the division so I can see where I'm going wrong please.

    Thank you
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  2. #2
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    Quote Originally Posted by Blu-Cherri View Post
    I hope this is in the correct section(i am in college and this is algebra..)

    I know this should be simple but I really can't spot where I'm going wrong.

    x^3+x^2+5x-2 is divisible by (x-2) I'm trying to completely factorise this by dividing this and then factorising the product. (this is the method i have to use for my C2 exam)

    Could someone show me the step through of the division so I can see where I'm going wrong please.

    Thank you
    The given term isn't factorable. But if you take

    (x^3+x^2 -5x-2) \div (x-2)=x^2+3x+1
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  3. #3
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    So I did do it correctly...so how do you work out the exact solutions of the equation?

    I guess i was using the wrong method completely
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  4. #4
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    (x-2) is a factor of x^3+x^2-5x-2 as demonstrated.

    If f(x)=x^3+x^2-5x-2, then f(2)=0

    Therefore x = 2 is a root (solution) to the polynomial function.

    Your factored equation is: f(x)=(x-2)(x^2+3x+1)

    The quadratic trinomial is not factorable, so use the quadratic formula to find the other two solutions
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  5. #5
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    Quote Originally Posted by Blu-Cherri View Post
    So I did do it correctly...so how do you work out the exact solutions of the equation?

    I guess i was using the wrong method completely
    First of all: This isn't an equation but a term. A quotient. I used long division:
    Code:
      (x^3 + x^2 - 5x - 2)  (x - 2) = x^2 + 3x + 1
     -(x^3 -2x^2)
     -------------
            3x^2 - 5x
          -(3x^2 - 6x)
         -------------
                    x - 2
                  -(x - 2)
                  ----------
                        0
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  6. #6
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    ah equation was in the question referring to f(x)=0 sorry i didn't make that clear.

    Thank you both for all the information, I think i'll be posted here most of this week leading up to my C2 exam >_<
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