Now you know that monomialscan be broken down right into their miscellaneous factors, and this is dubbed "factoringmonomials". We have the right to proceed a little further and begin to find commonfactors in POLYNOMIALS.

Actually, we will go for this reason faras to find the biggest COMMON MONOMIALFACTOR of every monomial in the polynomial. As soon as this is found, us willdivide it out of every monomial term.

You are watching: Common monomial factor examples with answers

It's sort of like solving apuzzle. You will be looking for the biggest missing piece that is commonto all the offered parts.

Here, let'stake a look in ~ one:

Ex 1:Find the greatest usual monomial factor of this polynomial, divide itout, and also rewrite the polynomial together a multiplication difficulty using thefactors girlfriend found. Now look at these three terms.Is there a element that will certainly divide EVENLY right into ALL THREE? If you have the right to findone, it will be a dubbed a "common" factor. Climate all us haveto do is make certain that it is the GREATEST usual factor.

After a bit of looking, wesee the the number 3 will divide right into all three terms. However, we can'tfind anything else that will divide into all three terms. So 3 need to bethe GREATEST common factor.

When us divide 3 out ofeach term and also then rewrite as a multiplication trouble it will look likethis: .

Ex 2: Factorthe polynomial into the product the its best monomial factor and also another trinomial.

Here the numericalcoefficients on each term room all even so 2 will absolutely divide intothem every without a remainder.

Also, we seethat over there is a power of "n" in each term. The smallest exponentin all 3 terms is the construed 1 top top the last term, so "n"will division evenly into each term in addition to the 2 found above. The makesthe GREATEST usual factor for this instance "2n".

When us divideit out and also rewrite the polynomial together a product the its greatest commonfactor and also another trinomial it will look prefer this: *NOTE:You can always check your factored prize by merely multiplying it. Ifyou don't obtain the initial polynomial back, you understand you are wrong.

YOU TRY:

Give these 3 a try. Writedown her answers before you click the price link.

Factor eachtrinomial into a product that its best monomial factor and another trinomial.  BACKto problems

Lookingfor the biggest monomial factor:(two variables allowed now...level 2)

Try these using the exact same techniqueas the one variable, greatest usual monomial factoring.

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Write under what friend think the"factored forms" will look like, then click the answers linkto see if you room correct.  