Question

How do you factor the trinomial `b^2-b-6`?

Answer 1

`(b-3)(b+2)`

Explanation:

In the given polynomial we can not use the identities to fatorize.
Let us chek this :
`color(blue)(X^2+SX+P=0)`
where:

We have to find two real numbers such that:
`color(blue)S =m+n`
`color(blue)P =m*n`

In the given polynomial
`m=-3 and n=2`
So, `S=-1 and P=-6`

`b^2-b-6`
`=(b-3)(b+2)`

Answer 2

`(b-3)(b+2)`

Explanation:

In order to factorise any quadratic expression in the form `ax^2 + bx+c, a !=0`, we need to find two numbers whose product gives `c` and whose sum gives `b`.

In this case, `b=-1` and `c=-6`. Since this is a relatively simple quadratic, one can easily figure out that the two numbers we need are `-3` and `2`:

`-3xx2=-6`
`-3+2=-1`

`b^2-b-6=(b-3)(b+2)`