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    If (x+2) is a factor of x^3+px^2-x-2 find p and the other factors when p has this value.

    I used synthetic division and identified that 4p+2x-10=0; 4p+2x=10

    HENCE

    2p+x=5

    Beyond that however, I am lost as to how I would go about finding the values of either P or X. My confusion stems from the fact that I have only been given one factor, namely, (x+2) and so it would appear that I am not able to utilise simultanteous equations to find the value of one term then substitute it into the equation to find the value of the other.
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    If (x-a) is a factor.

    f(a) = 0
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    (Original post by apronedsamurai)
    ...
    (x+2)(x^2+kx-1)=x^3+px^2-x-2

    Expand the brackets and compare coefficients of x^2 and x.
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    (Original post by apronedsamurai)
    If (x+2) is a factor of x^3+px^2-x-2 find p and the other factors when p has this value.

    I used synthetic division and identified that 4p+2x-10=0; 4p+2x=10

    HENCE

    2p+x=5

    Beyond that however, I am lost as to how I would go about finding the values of either P or X. My confusion stems from the fact that I have only been given one factor, namely, (x+2) and so it would appear that I am not able to utilise simultanteous equations to find the value of one term then substitute it into the equation to find the value of the other.

    I don't think you're supposed to use simultaneous equations
    I used synthetic division and directly found out that P=2
    And using that value and I found the other factor to be x^2-1
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    (Original post by binarythoughts)
    I don't think you're supposed to use simultaneous equations
    I used synthetic division and directly found out that P=2
    And using that value and I found the other factor to be x^2-1
    How did you find that p=2?

    When I used synthetic division, I used coeffecients 1 P -X and -2 with -2 as the input.

    so, 1, p-2; -2+4-x 4p-10+2x

    Even setting x to 0; in that case there is a discrepancy for P....
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    (Original post by apronedsamurai)
    How did you find that p=2?

    When I used synthetic division, I used coeffecients 1 P -X and -2 with -2 as the input.

    so, 1, p-2; -2+4-x 4p-10+2x
    Could you first confirm if it's right or not from the mark scheme ?
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    p=2; (x+1)(x-1)

    Is the answer given

    So yes, your correct; which I had suspected from the beginning. When I gave my response, I was showing my working to identify where I had made a mistake
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    (Original post by apronedsamurai)
    p=2; (x+1)(x-1)

    Is the answer given

    So yes, your correct; which I had suspected from the beginning. When I gave my response, I was showing my working to identify where I had made a mistake

    Alright. The thing is I'm not sure how you arrived to those figures. You should directly get p=2 if you put in -2 as the input and your other inputs are correct.
    You're final -8+4p=0
    0 because they've stated it's a factor so you can just insert that and directly find P
    Try and see if that helps
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    (Original post by binarythoughts)
    Alright. The thing is I'm not sure how you arrived to those figures. You should directly get p=2 if you put in -2 as the input and your other inputs are correct.
    You're final -8+4p=0
    0 because they've stated it's a factor so you can just insert that and directly find P
    Try and see if that helps
    Did you include X as a coeffecient?
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    (Original post by apronedsamurai)
    Did you include X as a coeffecient?
    Oh, I just figured out your mistake!
    You mentioned one of your values as -x
    that is incorrect as you are supposed to mention only the coefficients not x. So the coefficient is -1
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    (Original post by binarythoughts)
    Oh, I just figured out your mistake!
    You mentioned one of your values as -x
    that is incorrect as you are supposed to mention only the coefficients not x. So the coefficient is -1
    Thank you! . Can't believe I did that :|
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    (Original post by apronedsamurai)
    Thank you! . Can't believe I did that :|
    Glad I could help
 
 
 
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