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Math Help - Factorisation problem!

  1. #1
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    Factorisation problem!

    Is it possible to factorise this quadratic:
    x^2+2x+3

    Thanks in advance for any help!
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  2. #2
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    Hello,
    Quote Originally Posted by thebof1993 View Post
    Is it possible to factorise this quadratic:
    x^2+2x+3

    Thanks in advance for any help!
    Find yourself completing the square :

    x+2x+3=x+2x+1+2=(x+1)+2

    Difference of two squares ? Obviously not if you work on real numbers
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    Wow that was quick thank you. Hang on how does that give me 2x?
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  4. #4
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    Quote Originally Posted by thebof1993 View Post
    Is it possible to factorise this quadratic:
    x^2+2x+3

    Thanks in advance for any help!
    Do you remember the Perfect Squares rule?

    (a+b)^2 = a^2 + 2ab + b^2.

    x^2+2x+3 = x^2+2x+\left(\frac{2}{2}\right)^2-\left(\frac{2}{2}\right)^2+3
    =x^2+2x+1^2-1^2+3
    =(x+1)^2-1+3 by using the Perfect Squares Rule.
    =(x+1)^2+2
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  5. #5
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    Quote Originally Posted by thebof1993 View Post
    Is it possible to factorise this quadratic:
    x^2+2x+3

    Thanks in advance for any help!
    Do you know what a discriminant is? The discriminant here is less than zero. Therefore x^2+2x+3=0 has no real solutions therefore x^2+2x+3 can't be factorised using real numbers.
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  6. #6
    Moo
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    Quote Originally Posted by mr fantastic View Post
    Do you know what a discriminant is? The discriminant here is less than zero. Therefore x^2+2x+3=0 has no real solutions therefore x^2+2x+3 can't be factorised using real numbers.
    He doesn't know, I talked to him by PM.
    Also, he said it was maybe x+2x-3.

    sidenote
    Hang on how does that give me 2x?
    This question was because he thought that (a+b)=a+b
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  7. #7
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    Quote Originally Posted by Moo View Post
    He doesn't know, I talked to him by PM.
    Also, he said it was maybe x+2x-3.

    sidenote

    This question was because he thought that (a+b)=a+b
    If only they'd check such wonderful formulae by substituting a non-zero value for a and b .....
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