Question 152225
x^2-5x+6=(x-3)(x-2)


Explanation:

A 2nd degree polynomial (ax^2+bx+c) will factor, if factorisable, to form  (1) (dx+e)(fx+g). Now, if we apply foil to (1), we get eg+(ef+dg)x+df x^2

Now,
eg=c
ef+dg=b
df=a

In words, we want two numbers e,g such that e*g equal the constant term of the original polynomial.

Moreover, we want numbers d,f such that d*f equals the coefficient of the x^2 term in the original polynomial.

Finally, we want two numbers f,d such that ef+dg equals the coefficient of the x term in the original polynomial.

As you can see, e and g give us the most useful information. We find e and g by looking at the factors of c.




For your polynomial, c is 6. The factors of 6 are 1,2,3,6. 
Now, for your polynomial, a is 1. 1 is the only factor of 1.

So we need numbers out of 1,2,3,6 that add to equal -5. We can see right away that -2+-3=-5. So these must be our f and g. So it factors as (x-3)(x-2)