In an expression like (2•3)+4+(7y), why is 4 considered a factor?

[KennyKVJ]

Hello, I'm new here.

So in this short video, Sal Khan states that factors are the items being multiplied together in each term. But then he says 4 is considered a factor in the expression (2•3)+4+(7y). If factors are the items being multiplied together, why is 4 a factor even though it is a constant and not being multiplied by anything?

I hope I'm explaining my question properly. Thanks for reading this and helping out a confused student guys!

 

[HallsofIvy]

You are misunderstanding. He doesn't say 4 is a factor of \(\displaystyle 2\cdot 3+ 4+ 7y\).

After taking about the three "terms", \(\displaystyle 2\cdot 3\). \(\displaystyle 4\), and \(\displaystyle 7y\), he says that "2" and "3" are factors of \(\displaystyle 2\cdot 3\), that \(\displaystyle 7\) and \(\displaystyle y\) are factors of \(\displaystyle 7y\), and that \(\displaystyle 4\) is a factor of \(\displaystyle 4\) (because it can be written \(\displaystyle 4\cdot 1\), not a factor of the entire expression.

Notice that the "factors" and how many factors a term has is a matter of "how it is written", not its actual numeric value. We could have as easily written \(\displaystyle 2\cdot 3\) as "6" so our expression was \(\displaystyle 6+ 4+ 7y\) and now say that the first and second terms have only one factor. Or, since \(\displaystyle 6+ 4= 10\), write this as \(\displaystyle 10+ 7y\) and say that there are only two "terms", 10 and 7y.

 

[Deleted member 4993]

Hello, I'm new here.

So in this short video, Sal Khan states that factors are the items being multiplied together in each term. But then he says 4 is considered a factor in the expression (2•3)+4+(7y). If factors are the items being multiplied together, why is 4 a factor even though it is a constant and not being multiplied by anything?

I hope I'm explaining my question properly. Thanks for reading this and helping out a confused student guys!

The "4" in the 1st expression is a "term". We can write:

4 = 4 [times] 1 = 4 * 1

Thus we can say 4 is a factor of 4. A bit redundant, but for the sake of completeness, we can stick with that "saying".

 

[KennyKVJ]

You are misunderstanding. He doesn't say 4 is a factor of \(\displaystyle 2\cdot 3+ 4+ 7y\).

After taking about the three "terms", \(\displaystyle 2\cdot 3\). \(\displaystyle 4\), and \(\displaystyle 7y\), he says that "2" and "3" are factors of \(\displaystyle 2\cdot 3\), that \(\displaystyle 7\) and \(\displaystyle y\) are factors of \(\displaystyle 7y\), and that \(\displaystyle 4\) is a factor of \(\displaystyle 4\) (because it can be written \(\displaystyle 4\cdot 1\), not a factor of the entire expression.

Notice that the "factors" and how many factors a term has is a matter of "how it is written", not its actual numeric value. We could have as easily written \(\displaystyle 2\cdot 3\) as "6" so our expression was \(\displaystyle 6+ 4+ 7y\) and now say that the first and second terms have only one factor. Or, since \(\displaystyle 6+ 4= 10\), write this as \(\displaystyle 10+ 7y\) and say that there are only two "terms", 10 and 7y.

So is 4 considered a factor in the second term because it is implicitly 4 x 1 = 4 ?
Do we consider the 4 a constant? If so, can a constant be considered a factor? Thanks for replying!

 

[Deleted member 4993]

So is 4 considered a factor in the second term because it is implicitly 4 x 1 = 4 ?
Do we consider the 4 a constant? If so, can a constant be considered a factor? Thanks for replying!

Yes...

 

[KennyKVJ]

Yes...

Thanks dude, I appreicate the help

 

[Steven G]

Terms, not inside parenthesis, are separated my by addition and subtraction signs. Given a single term, what is being multiplied or divided are called terms. If 4 is a term then it is splitting hairs by also calling it a factor. I wouldn't.

It reminds me when some people call the number 7.2 a non-ending decimal number. It is not wrong as 7.2 = 7.2000000......