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    How do you factorise x3 + x2 - 5x - 2 = 0

    Thanks in advance :hat2:
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    (Original post by Tilly-Elizabeth)
    How do you factorise x3 + x2 - 5x - 2 = 0

    Thanks in advance :hat2:
    The usual way is to "spot" a factor and the use one of the division methods to find the quadratic

    Since the constant is -2 the factors to consider would be 1, -1, 2, -2

    Have you used the factor or remainder theorem
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    (Original post by TenOfThem)
    The usual way is to "spot" a factor and the use one of the division methods to find the quadratic

    Since the constant is -2 the factors to consider would be 1, -1, 2, -2

    Have you used the factor or remainder theorem
    (x-2) is a factor of the equation and when I use the factor theorem it substitutes perfectly. Ohhh it just clicked what I have to do.

    One second I'm going to work it out and I'll see if I have it right.

    Thanks
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    (Original post by Tilly-Elizabeth)
    (x-2) is a factor of the equation and when I use the factor theorem it substitutes perfectly. Ohhh it just clicked what I have to do.

    One second I'm going to work it out and I'll see if I have it right.

    Thanks
    ok

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    Oh my god you're so cute Tilly
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    (Original post by TenOfThem)
    ok

    I have confused myself.

    I have (x-2) which is one of the brackets so I'll have (x-2)(x-?)(x-?) = 0

    So how do I remove the other two brackets?
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    (Original post by Tilly-Elizabeth)
    I have confused myself.

    I have (x-2) which is one of the brackets so I'll have (x-2)(x-?)(x-?) = 0

    So how do I remove the other two brackets?
    x^3 + x^2 - 5x - 2 = (x - 2)(x^2 + bx + 1)

    You can either use inspection or multiply out the RHS and compare coefficients

    Then, when you have your quadratic you can check to see if that factorises
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    (Original post by TenOfThem)
    x^3 + x^2 - 5x - 2 = (x - 2)(x^2 + bx + 1)

    You can either use inspection or multiply out the RHS and compare coefficients

    Then, when you have your quadratic you can check to see if that factorises
    Ah right.

    So if I use algebraic division I get x2 + 3x + 1

    If I use the formula I get x=(-3-√5)/2 and x=(-3+√5)/2

    So I should get:

    (x-2)(x + 2.62)(x + 0.38) = 0
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    (Original post by Tilly-Elizabeth)
    Ah right.

    So if I use algebraic division I get x2 + 3x + 1

    If I use the formula I get x=(-3-√5)/2 and x=(-3+√5)/2

    So I should get:

    (x-2)(x + 2.62)(x + 0.38) = 0
    It depends on what the question asks

    If you want to factorise then the answer is

    (x-2)(x^2+3x+1)

    If it asks you to solve

    x^3 + x^2 - 5x - 2 = 0

    Then your solutions are x = 2 or x = \dfrac{-3\pm\sqrt5}{2}
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    (Original post by TenOfThem)
    It depends on what the question asks

    If you want to factorise then the answer is

    (x-2)(x^2+3x+1)

    If it asks you to solve

    x^3 + x^2 - 5x - 2 = 0

    Then your solutions are x = 2 or x = \dfrac{-3\pm\sqrt5}{2}
    Oh I read it wrong it wanted the solutions.

    Thank you for your help!
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    Have you heard of the remainder theorem? This is what my teacher taught us for factorising polynomials. You can Google it if this website doesn't help, it's only one of many that exist

    http://www.purplemath.com/modules/remaindr.htm
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    Few ways of doing this. Say r is a root, then by the factor theorem (x - r) is a factor. Equivalently, f(r) = 0.

    After you've guessed one, you can compare coefficients, get a quadratic in x (has to be a quadratic as the product of a linear and quadratic term is a cubic term), and then factorise (it's not necessarily factorisable) to get three linear terms.
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    (Original post by Zen-Ali)
    ...
    Your sig makes it seem like you know what you're talking about.
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    (Original post by Khallil)
    Your sig makes it seem like you know what you're talking about.
    So does my peepee.
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    (Original post by Zen-Ali)
    ...
    l000000000l
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    (Original post by Khallil)
    l000000000l
    :sexface:

    Spoiler:
    Show
    Enough derailing.
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    (Original post by Khallil)
    Your sig makes it seem like you know what you're talking about.

    Did he copy that signature from a member on here? He had it like 2 years ago? I think his name was Zake or Zakee?
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    (Original post by Prince.of.Maths)
    ...
    Zakee, is this your dupe account?
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    (Original post by Khallil)
    Zakee, is this your dupe account?

    No sorry, my name is pipo.

    I'm referred to as andres contreras-hip from my youtube channel.
 
 
 
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