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Math Help - Can you help me factor out these polynomials the complete way

  1. #1
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    Can you help me factor out these polynomials the complete way

    What I mean by the complete way is this example:
    x^2 - 12x + x - 12
    x^2 - 12x + x - 12
    x (x - 12) - 1(x - 12)
    (x - 12) (x + 1)
    x^2 - x + 12x - 12
    x^2 + 11x - 12

    These are the problems that I'm stuck on:

    1. 5x^2 - 80
    2. x^2 - 100
    3. x^3 - 3x^2 + 4x
    4. 81x^2 - 1
    5. x^2 + 13x - 30
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  2. #2
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    Re: Can you help me factor out these polynomials the complete way

    Quote Originally Posted by AmberxRebecca View Post
    What I mean by the complete way is this example:
    x^2 - 12x + x - 12
    x^2 - 12x + x - 12
    x (x - 12) - 1(x - 12)
    (x - 12) (x + 1)
    x^2 - x + 12x - 12
    x^2 + 11x - 12

    These are the problems that I'm stuck on:

    1. 5x^2 - 80
    2. x^2 - 100
    3. x^3 - 3x^2 + 4x
    4. 81x^2 - 1
    5. x^2 + 13x - 30
    1. You need to use the Difference of Two Squares: \displaystyle \begin{align*} a^2 - b^2 = (a - b)(a + b) \end{align*}

    \displaystyle \begin{align*} 5x^2 - 80 &= 5\left(x^2 - 16\right) \\ &= 5\left(x^2 - 4^2\right) \end{align*}

    2. See 1.

    3. \displaystyle \begin{align*} x^3 - 3x^2 + 4x &= x\left(x^2 - 3x + 4\right) \end{align*}

    Now factorise the Quadratic as you normally would.

    4. See 1.

    5. The two numbers you are looking for are 15 and -2.
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