Question

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

Answer 1

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

Answer 2

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)`