Find the factors of 6x2−13x+6=0
(3x–2)(2x–3)
6x2−13x+6 ----->(1)
Using the method of splitting the middle term.
x term is the sum of two factors and product equal to the last term.
Here a = 6,b = -13,and C = 6
a.c = Product of 6 and 6 = 36
Factors of 36 = 2,18
= 3,12
= 4,9
Only the factors 4 and 9 gives 13 ⟶ (4 + 9)
For -13 , both the factors have negative sign. (- 4 - 9 = - 13)
Equation (1) ⇒ 6x2−4x−9x+6
⇒2x(3x–2)–3(3x–2)
⇒(3x–2)(2x–3) are the factors.