# Math Help - Factorisation problem!

1. ## Factorisation problem!

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

Thanks in advance for any help!

2. Hello,
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

3. Wow that was quick thank you. Hang on how does that give me 2x?

4. 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.
$=(x+1)^2+2$

5. 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.

6. 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
Hang on how does that give me 2x?
This question was because he thought that (a+b)²=a²+b²

7. 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 .....