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......