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Thread: I forgot how to reverse foil (such as X^2 + 2X + 2)

  1. #1
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    I forgot how to reverse foil (such as X^2 + 2X + 2)

    Take this equation:

    X^2+2X+2

    If you reverse foil (I remember how to foil I think)

    would you get:

    (X+1)(X+1)

    ? Just a guess.

    X^2+X+X+1

    Nope, that doesn't work.

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    Quote Originally Posted by Quick View Post
    X^2 + 2X + 2

    If you

    [tex]\text{reverse f}\text{oil}[/tex]

    would you get:

    (X+1)(X+1)

    ? Just a guess.

    X^2+X+X+1

    Nope, that doesn't work.
    The common term for that phrase is the verb 'factor'. Factoring is the reverse of expanding (aka: multiplying out, or 'foiling, in this instance').

    The given quadratic polynomial does not factor nicely. The factorization is:

    (x + 1 - i)(x + 1 + i)

    where symbol i represents the square root of -1 (aka the imaginary unit).

    There's a shortcut for determining whether a quadratic polynomial (Ax^2+Bx+C) factors nicely. Determine its Discriminant (B^2-4AC). If the Discriminant is not a perfect square, then the polynomial does not factor nicely.
    Last edited by mmm4444bot; 01-22-2018 at 01:53 AM. Reason: used \text{} to prevent auto-linking from interfering with my blood!!
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    Quote Originally Posted by mmm4444bot View Post
    The common term for that phrase is the verb 'factor'. Factoring is the reverse of expanding (aka foiling, in this instance).

    The given quadratic polynomial does not factor nicely. The factorization is:

    (x + 1 - i)(x + 1 + i)

    where symbol i represents the square root of -1 (aka the imaginary unit).

    There's a shortcut for determining whether a quadratic polynomial (Ax^2+Bx+C) factors nicely. Determine its Discriminant (B^2-4AC). If the Discriminant is not a perfect square, then the polynomial does not factor nicely.
    Thanks for answering.

    Is there a way to find the lowest common denominator to factor?

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Quick View Post
    Is there a way to find the lowest common denominator to factor?
    I'm not sure that I understand. There's no denominator, in your example.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    Quote Originally Posted by mmm4444bot View Post
    I'm not sure that I understand. There's no denominator, in your example.
    OK, I will try and come up with an example.

    X^2+40X+6

    X^2, 40, and 6 all have the number 2 in common. X^2 is just X times X, so you really don't need to manipulate anything there.

    Could you use 2 to find the lowest common denominator to factor the rest of the equation out?

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    Quote Originally Posted by Quick View Post
    OK, I will try and come up with an example.

    X^2+40X+6

    X^2, 40, and 6 all have the number 2 in common. X^2 is just X times X, so you really don't need to manipulate anything there.

    Could you use 2 to find the lowest common denominator to factor the rest of the equation out?
    You may mean "greatest common factor" rather than "lowest common denominator".

    But 2 is not a factor of x^2; it's an exponent, which is an entirely different thing.

    This polynomial, like the first, can't be factored over the integers (that is, factored into factors containing only integers).

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    Quote Originally Posted by Dr.Peterson View Post
    You may mean "greatest common factor" rather than "lowest common denominator".

    But 2 is not a factor of x^2; it's an exponent, which is an entirely different thing.

    This polynomial, like the first, can't be factored over the integers (that is, factored into factors containing only integers).
    Thank you for your answer. It answers my question.

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    Quote Originally Posted by Denis View Post
    You can look at it this way:
    your math teacher makes up a similar problem:
    (2x + 3) * (x + 7) = 2x^2 + 17x + 21

    Then tells you: factor 2x^2 + 17x + 21
    Your answer should be (2x + 3)(x + 7)
    Thanks, I think I have the basic concept down now.

    You have to take the equation as a whole and you can't split it up into different sections. That is what I was trying to figure out.

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    To say it better, you can't really 'mix and match' with addition and multiplication to find a greatest common factor.

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    But I was thinking along these lines:

    X^2+40X+6

    x^2+2(20x+3)

    But I don't think this actually changes the equation to the point that you can Factor from that point...

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