How do you factor #x^2-5x+6=0#?

1 Answer
Apr 30, 2016

Answer:

#color(green)((x-3)(x-2)# is the factorised form of the expression.

Explanation:

#x^2 - 5x + 6 = 0#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*6 = 6#

AND

#N_1 +N_2 = b = -5#

After trying out a few numbers we get #N_1 = -2# and #N_2 =-3#

#(-2)*(-3) = 6#, and #(-2) +(-3)= -5#

#x^2 - 5x + 6 =x^2 - 2x -3x + 6 #

# = x (x-2) -3 (x -2 )#

#(x-2)# is a common factor to each of the terms

#=color(green)((x-3)(x-2)#