David W. answered • 02/24/16
Tutor
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Repeat questions (this one both today and yesterday) are like repeat answers – You might try rephrasing rather than just repeating.
So, let’s take a look at the problem statement and try to rephrase it. Then, we can rephrase our answer.
That process might actually help you to understand.
Math requires definitions, procedures, etc. First, we must understand Greatest Common Factor (GCF).
And before that, we must understand Factor(You might already know what greatest and common mean, but I don’t always assume that).
A Factoris a number or quantity that, when multiplied by another, produces a given expression.
Common means shared between the two. Greatestis a synonym for largest.
In this problem, the two values are 12b and 3. They are added to form the Expression 12b+3. This expression is also the product of two factors(what are they? – that’s the question).
One method of finding the GCG is to list all the factors, then compare the lists to find the greatest(sorry, if this sounds really redundant, but that’s how math is).
Factorsof 12: 1, 2, 3, 4, 6, 12
[those are all the numbers that divide evenly into 12]
Factorsof 6: 1, 2, 3, 6
GCFof 12 and 6: 6
O.K., the problem –
Factorsof 12b: 1, 2, 3, 4, 6, 12, b [a lot like the above]
Factorsof 3: 1, 3
GCFof 12b and 3: 3 (note: b might be larger, but we don't know)
Now, add the terms:
Factorsof (12b+3): 1, 3, (4b+1), (12b+3)
These are all the factors that we can multiply to get (12+3).
“To factor” means to break an expression apart into terms that we multiply to get that expression. So, the answer to the problem is: 3(4b+1).
