1. ## The Impossible Factorisation

My friend and I are arguing again, about Maths (How cool are we?).

Please, just assure me (and him), that you cannot factorise the equation:

$x^2 + 100$

So that there are two brackets, each with a value of $x$ in.

2. Originally Posted by Bench.
Please, just assure me (and him), that you cannot factorise the equation:
$x^2 + 100$
That's not an equation. ALL equations have an = sign.

(x+10)(x+10) - 20x

3. It can't be factorized over $\mathbb{R}$, but it can be factorized over $\mathbb{C}$:

$x^2+100=(x-10i)(x+10i)$

4. Originally Posted by red_dog
It can't be factorized over $\mathbb{R}$, but it can be factorized over $\mathbb{C}$:

$x^2+100=(x-10i)(x+10i)$

What is factorising over "C"?

5. R is the set of numbers you encounter in everyday life. This includes whole numbers, fractions and numbers like Pi. C is the set of all those and the complex numbers, which includes i, the root of -1.

6. Fantastic. What does C and R stand for, if they stand for anything?

7. C stands for Complex, R for Real. (I think)

8. Originally Posted by Bench.
Fantastic. What does C and R stand for, if they stand for anything?
You may want to do a search:

N - natural numbers

Z - integers

Q - rational numbers

R - real numbers

C - complex numbers

Its important to know what each set includes and its properties.