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Math Help - Polynomial help?

  1. #1
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    Smile Polynomial help?

    Hey!
    Im going through some polynomial questions as revision but i've come across one that's stumped me. I've tried it over and over but just can't see where i'm going wrong. The question is as follows:

    The polynomial: f(x)= px^3 - x^2 + qx - 6
    has x-3 as a factor. When f(x) is divided by x-2, the remainder in -20.

    (a) Show that p=2 and find the value of q
    (b) Factorise f(x)

    For the first part i've come out with p=2, which is right, and q=-13. However, this doesn't factorise well in the second part.
    Any help would be great! Thanks for reading!
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by kim_lloyd25 View Post
    Hey!
    Im going through some polynomial questions as revision but i've come across one that's stumped me. I've tried it over and over but just can't see where i'm going wrong. The question is as follows:

    The polynomial: f(x)= px^3 - x^2 + qx - 6
    has x-3 as a factor. When f(x) is divided by x-2, the remainder in -20.

    (a) Show that p=2 and find the value of q
    (b) Factorise f(x)

    For the first part i've come out with p=2, which is right, and q=-13. However, this doesn't factorise well in the second part.
    Any help would be great! Thanks for reading!
    Everything looks good to me. After dividing by (x-3), you're left with

    2x^2+5x+2, which factors into (2x-1)(x+2)
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