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

2 Answers
Oct 12, 2016

#(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)#

Oct 12, 2016

#(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)#