i need help understanding this problem

Question

Factor the polynomial completely.

 

ab−3a−5b+15

Answer 1

What they are trying to do is show you that no matter which way you group the terms you get the same answer.

For this, we will leave the problem as is... but adding grouping symbols.

(ab-3a) (-5b+15) Now looking at each group we factor out (divide) what they have in common

Group 1: We factor out the a and it looks like this.... a(b-3)

Group 2: Because the lead term is a negative, usually we will pull out the - w/ the 5 and this is what it looks like... -5(b-3)

 

Now our problem looks like this...

a(b-3) -5(b-3) Since they both share a (b-3)... we will group the (a) and the (-5) together in a set of () and technically we are factoring the (b-3) out of both.... (a-5)(b-3) and that is your answer.