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Struggling to factorise a cubic polynomial with one known root watch

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    Going through an old test and am stuck on this question:

    The cubic polynomial 2x^3 + kx^2 - x + 6 is denoted by f(x). It is given that (x+1) is a factor of f(x)

    Show that k = -5, and factorise f(x) completely.


    I've done the 'show k=-5' bit fine but am just going round in circles trying to factorise it, help would be appreciated xo
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    This is my method. I'm going to add a picture with some annotations at that will be easiest
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    (Original post by Arcade22)
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    Thank you so much!!
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    (Original post by emilyrose2001)
    Going through an old test and am stuck on this question:

    The cubic polynomial 2x^3 + kx^2 - x + 6 is denoted by f(x). It is given that (x+1) is a factor of f(x)

    Show that k = -5, and factorise f(x) completely.


    I've done the 'show k=-5' bit fine but am just going round in circles trying to factorise it, help would be appreciated xo
    Are you aware of the Factor Theorem?
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    (Original post by Arcade22)
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    Please remove your full solution
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    (Original post by RDKGames)
    Are you aware of the Factor Theorem?
    Yeah I was just lost on how exactly to use it
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    you can do long division. divide f(x) by ( x + 1 ) to get a quadratic. this will usually factorise into two brackets.
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    (Original post by emilyrose2001)
    Yeah I was just lost on how exactly to use it
    It says that if some number a is root of your polynomial, then the linear expression (x-a) must divide the polynomial.

    Here, you already used this without even thinking to find k by substituting in -1. Anyhow, the theorem says (x+1) divides the cubic. So after you find the k, you can use long division to determine (your cubic)/(x+1) which yields a quadratic you can factorise further
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    (Original post by RDKGames)
    Please remove your full solution
    Sorry - it's always easier to understand when it's written as opposed to typing it out. However, if enough people want me to take down my working, then I'll happily oblige
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    (Original post by emilyrose2001)
    Yeah I was just lost on how exactly to use it
    That's fine it's weird to get used to
    Factor theorem is what's in my working. Write it, expand it, then fill in the letters with numbers. At the end it's just a nice factorisation
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    Thanks both of you
 
 
 
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