Factorise x2–5x+6 by using the Factor Theorem.
(x–2)(x–3)
Let p(x)=x2–5x+6.
Let factors be (x−a) and (x−b)
So, p(x)=(x–a)(x–b)
⇒p(x)=x2–bx–ax+ab
On comparing the constants,
we get ab = 6.
The factors of 6 are 1, 2 and 3.
Now, p(2)=22–(5×2)+6=4–10+6=0.
So, (x–2) is a factor of p(x).
Also, p(3)=32–(5×3)+6=9–15+6=0
So, (x–3) is also a factor of x2–5x+6
Therefore, x2–5x+6=(x–2)(x–3)