# Factorisation problem!

• Sep 10th 2008, 09:25 AM
thebof1993
Factorisation problem!
Is it possible to factorise this quadratic:
x^2+2x+3

Thanks in advance for any help!
• Sep 10th 2008, 09:27 AM
Moo
Hello,
Quote:

Originally Posted by thebof1993
Is it possible to factorise this quadratic:
x^2+2x+3

Thanks in advance for any help!

Find yourself completing the square :

x²+2x+3=x²+2x+1+2=(x+1)²+2

Difference of two squares ? Obviously not if you work on real numbers :)
• Sep 10th 2008, 09:30 AM
thebof1993
Wow that was quick thank you. Hang on how does that give me 2x?
• Sep 10th 2008, 05:34 PM
Prove It
Quote:

Originally Posted by thebof1993
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.
$=(x+1)^2+2$
• Sep 10th 2008, 08:52 PM
mr fantastic
Quote:

Originally Posted by thebof1993
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.
• Sep 10th 2008, 11:00 PM
Moo
Quote:

Originally Posted by mr fantastic
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 x²+2x-3.

sidenote
Quote:

Hang on how does that give me 2x?
This question was because he thought that (a+b)²=a²+b² :)
• Sep 10th 2008, 11:10 PM
mr fantastic
Quote:

Originally Posted by Moo
He doesn't know, I talked to him by PM.
Also, he said it was maybe x²+2x-3.

sidenote

This question was because he thought that (a+b)²=a²+b² :)

If only they'd check such wonderful formulae by substituting a non-zero value for a and b .....