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

2 Answers
Mar 13, 2018

take the product to be 6 and sum to be -5
so you will get the factors as #-2# and #-3#
so you take like
#x^2 -2x -3x +6#
then take the common factor from any two terms
#x(x-2)-3(x-3)#
#rArr(x-2)(x-3)#
#x=2# & #x=3 # are the factors of this equation

Mar 13, 2018

Answer:

Use middle term splitting.
# x^2-5x+6=(x-2)(x-3)#

Explanation:

Consider the given equation: #x^2-5x+6#

Here
sum = -5
product = 6

Consider the pair of numbers which when multiplied gives a product (6) and sum (-5).

Since the product is positive, either both numbers should be positive or both numbers should be negative.

The options are:
#1*6=6# but #1+6=7# (Not required pair)
#(-1)*(-6)=6# but #(-1)+(-6)=-7#(Not required pair)
#2*3=6# but #2+3=5# (Not required pair)
#(-2)*(-3)=6# also #(-2)*(-3)=-5# (Required pair)

So,
#x^2-5x+6=(x^2-2x-3x+6)#

Now, group the terms.
Then,
#x^2-5x+6=(x^2-2x)-(3x-6)#
#=x(x-2)-3(x-2) #
#=(x-2)(x-3)#