Regarding issue in factors of a term in Algebraic expression.

[Mr. Lucky_45]

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

 

[Deleted member 4993]

While writing factors of each terms in an Algebraic Expression why the constant value is not further factorised ?View attachment 34131

You can write those as 2*2 (=4) and 5*2 (=10). I would. But I would NOT create separate branches for those. Then the tree diagram can become too congested you would not see the tree for the branches.

 

[Dr.Peterson]

While writing factors of each terms in an Algebraic Expression why the constant value is not further factorised ?View attachment 34131

It depends on context, particularly on what your goal is. This is not the only way to do this (and their tree form is not a standard form I have seen elsewhere). This is their choice, for their own reasons.

If the goal were to factorize the entire expression by finding the GCF of all the terms, it would be wrong not to break 10 into 2*5. That must not be their goal.

What is the context?

In any case, since what they are doing is subjective in this sense, all you can do is to take their definition of the process and follow it. Hopefully in the end you will see how the particular choices they have made end up being useful.

My guess is that they may eventually have you factorize the numerical coefficients too!

 

[Steven G]

I too would have factored the 4 and 10. I'm not sure why the author did not. I do like that the author uses factors and terms. I feel that is the way to teach this material.

 

[blamocur]

While writing factors of each terms in an Algebraic Expression why the constant value is not further factorised ?View attachment 34131

My guess is that they are working with the [imath]\mathbb R[x][/imath] ring, i.e. the coefficients are treated as real numbers even though they happen to be integers in this example.

 

[Cubist]

The source of OP's attachment seems to be online. I just typed some of the text into Google and came across this:- http://home-tutor.in/resources/flip/ncert/7/gemh1dd/files/basic-html/page243.html

You can manually edit the URL to obtain the page number of your choice. This particular section seems to begin on page 241:- http://home-tutor.in/resources/flip/ncert/7/gemh1dd/files/basic-html/page241.html and is titled, "Algebraic expressions". It simply seems to be breaking an expression down into its written constituent parts (I don't have time to fully read it at the moment)

 

[lookagain]

My guess is that they are working with the [imath]\mathbb R[x][/imath] ring, i.e. the coefficients are treated as real numbers even though they happen to be integers in this example.

The content of the OP's post is beginning algebra. Your mathematical ring material comment is at some outside/upper level.