To find all possible factors of a Monomial.

Mr. Lucky_45 said:
What are all possible factors of Monomial 4xy where x and y belongs to R(real numbers)?
Click to expand...
Can you calculate all possible factors of 4 * 15 * 77 ?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Mr. Lucky_45 said:
What are all possible factors of Monomial 4xy where x and y belongs to R(real numbers)?
Click to expand...
I believe this is a confusing question. The word “factor” is used in mathematics for several very closely related meanings.

The most general meaning relates to the components of a “product,” where “product” means the result of multiplication. If we interpret “factor” in your question in that most general sense, it is impossible to answer because every real number has an infinite number of real factors. So we can eliminate that meaning as making the question impossible to answer.

”Factor” is also used with respect to positive integers as shorthand for “prime factors.” Because the question does not say “prime factors“ and because you seem to be studying factors in the context of useful decomposition of products, my guess is that they mean integer factors with respect to the four in the question. Can you list the integers (positive and negative) that divide four evenly?

With respect to algebraic expressions, “factor” is often used to mean one of several ”simpler” or “more useful” algebraic expressions that when multiplied together give the original expression. When we look at 4xy, we see that it is a product, the result of multiplication of a numeral, namely 4, times an algebraic expression, namely xy. But xy also represents a product. Can you break the algebraic expression xy into even “simpler“ algebraic expressions that when multiplied together generate xy as the result?

The mention of real numbers is just unnecessary verbiage.
 
Mr. Lucky_45 said:
What are all possible factors of Monomial 4xy where x and y belongs to R(real numbers)?
Click to expand...
As was pointed out in your first thread, the answer may depend on context. What is "possible" depends on what you are allowed to do! If this is related to that other question, I think they probably expect you to make a term from each subset of {4,x,y}, because factors of 4 over the integers are irrelevant to real numbers..

For context, please tell us whether you are studying beginning algebra, as you have indicated, or something more advanced; and what topics have been taught recently. Also, show us any example you were given in which "all possible factors" were required.

Also, please show us your own thoughts, as requested, so we can see what issue you are concerned about.
 
Otis said:
Agree! And, I would say {1, 4, x, y}. ;)
[imath]\;[/imath]
Click to expand...
Not really. The empty set is also a subset, and corresponds to 1, the way I'm thinking. We don't need both 1 and 4 in any factor.

But I really want to see more about what is being taught.
 
Dr.Peterson said:
Not really. The empty set is also a subset, and corresponds to 1, the way I'm thinking. We don't need both 1 and 4 in any factor.

But I really want to see more about what is being taught.
Click to expand...
ABSOLUTELY. But i do suspect that when they say all possible factors of four, they mean all possible integer factors of four, of which there are six. I am not sure of course, but if this is all an introduction to factoring quadratics, that would make sense.
 
JeffM said:
ABSOLUTELY. But i do suspect that when they say all possible factors of four, they mean all possible integer factors of four, of which there are six. I am not sure of course, but if this is all an introduction to factoring quadratics, that would make sense.
Click to expand...
I'd agree, if not for the other thread,

Regarding issue in factors of a term in Algebraic expression.

While writing factors of each terms in an Algebraic Expression why the constant value is not further factorised ?
www.freemathhelp.com

There, it appears that they don't factor the coefficient. But all we're doing is guessing, without further data.
 
Dr.Peterson said:
The empty set is also a subset, and corresponds to 1 … We don't need both 1 and 4 in any factor.
Click to expand...
My point is to not forget listing 1 and 4xy as factors of the monomial 4xy. (I didn't mean to hint at anything else.) I ought to have written, "I would say to the OP" or simply:

(1)(4xy) = 4xy

:)
[imath]\;[/imath]
 
You must log in or register to reply here.
Top