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Math Help - Factoring Trinomials

  1. #1
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    Red face Factoring Trinomials

    Could anyone help me with this. I know its easy but, I completely forgot everything about math last year. (grade 11 now)

    Practice Factoring Trinomials.

    determine two values of c so that each expression can be factored.

    a) x^2 + 4x + c
    b) x^2 - 9x + c

    and

    Determine expressions to represent the dimensions of this rectangular prism.

    Volume is x^3 + 5x^2 + 6x.

    please explain ? thanks !
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Factoring Trinomials

    In general,
    x^2 + bx + c can be factored into (x + p)(x + q) when:
    1) p*q = c, and
    2) p + q = b

    So for your first question, we require that p + q = 4. So find two numbers with sum = 4 (there will be infinite solutions). For example
    p = 104, q = -100 gives c = p*q = -10400
    So x^2 + 4x + c = x^2 + 4x - 10400 = (x + 104)(x - 100)
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  3. #3
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    Re: Factoring Trinomials

    Quote Originally Posted by Thenewguy View Post
    Could anyone help me with this. I know its easy but, I completely forgot everything about math last year. (grade 11 now)

    Practice Factoring Trinomials.

    determine two values of c so that each expression can be factored.

    a) x^2 + 4x + c
    b) x^2 - 9x + c

    and

    Determine expressions to represent the dimensions of this rectangular prism.

    Volume is x^3 + 5x^2 + 6x.

    please explain ? thanks !
    Try completing the square for a) and b)

    \displaystyle \begin{align*} x^2 + 4x + c &= x^2 + 4x + 2^2 - 2^2 + c \\ &= (x + 2)^2 - 4 + c \\ &= (x + 2)^2 - (4 - c) \\ &= (x + 2)^2 - \left(\sqrt{4 - c}\right)^2 \\ &= \left(x + 2 - \sqrt{4-c}\right)\left(x + 2 + \sqrt{4-c}\right) \end{align*}

    So in order for this quadratic to be factorised over the integers, \displaystyle 4 - c needs to be a perfect square. What are some values of \displaystyle c that will enable this?
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  4. #4
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    Re: Factoring Trinomials

    ax^2+bx+c can be factored if and only if sqrt(b^2-4ac) is a rational number.
    in you above 2 example:
    a) x^2 + 4x + c,
    It can be factored if c = 4 or 3 or 0..etc...
    x^2+4x+4 = (x+2)^2, x^2+4x+3 = (x+3)(x+1), x^2+4x+0 = x(x+4)

    b) x^2 - 9x + c
    It can be factored if c = -10 or 20 or 0..etc...
    x^2-9x-10 = (x-10)(x+1), x^2-9x+20= (x-4)(x-5), x^2-9x+0 = x(x-9)


    for the last question, factorize x^3 + 5x^2 + 6x first.
    =x^3 + 5x^2 + 6x
    =x(x^2+5x+6), you know what to do next
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  5. #5
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    Re: Factoring Trinomials

    Thank you Piscoau, Prove it, The Chaz. I understand now xD.
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