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Math Help - Factorising equations

  1. #1
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    Unhappy Factorising equations

    a) x(squared) - 11x + 30
    b) a(squared) - 7a + 10
    c) b(squared) + 10b + 24
    d) y(squared) - 9y + 20
    e) p(squared) -7p -18
    f) x(cubed) + x(squared) - 6x

    Help on these would be much appreciated, thank you
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  2. #2
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    Quote Originally Posted by jimmybob View Post
    a) x(squared) - 11x + 30
    b) a(squared) - 7a + 10
    c) b(squared) + 10b + 24
    d) y(squared) - 9y + 20
    e) p(squared) -7p -18
    f) x(cubed) + x(squared) - 6x

    Help on these would be much appreciated, thank you

    Hi,

    If
    x + px + q = (x + a)(x + b)

    then q = a * b
    and p = a + b

    Therefore: if q is positive then a and b have the same sign (both + or both -)
    if q is negative then a and b have different signs.

    Use these hints to do:

    a) x - 11x + 30 = (x - 5)(x - 6)

    b) a - 7a + 10 = (a - 5)(a - 2)

    c) b + 10b + 24 = (b + 4)(b + 6)

    d) y - 9y + 20 = (y - 5)(y - 4)

    e) p -7p -18 = (p - 9)(p + 2) That's the first problem where the last summand is negative. Therefore the numbers a and b you are looking for must have different signs. The absolute value of the negative number must be greater than the positive one because the coefficient of x is negative.

    f) x + x - 6x = x(x + x - 6) = x(x - 2)(x + 3) Factor out the x. In the bracket is a quadratic term which can be factorized as usual

    EB


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