I have a math problem that is possibly a brain glitch or possibly something I don’t understand.

For the expression 5x+3y+10

It says to identify the factors (coefficient and sum of terms)

What are they saying? I don’t see a factor here we can take out

@Bronwyn me neither!
@Bronwyn @smellsofbikes me threither. You could rewrite it in various ways, but I don’t see anything that would not be horribly twisted to fit.
@UweHalfHand @smellsofbikes I’m very disappointed in this curriculum

@smellsofbikes @Bronwyn What is this curriculum?

Looking at this, I wonder if it is asking “identify the pieces of this expression which are terms, … factors”? In which case, I would answer as you did that there are 3 terms, and for factors I would say 5, x, 3, y (can’t see the original now as I’m typing, hope I didn’t mess anything up!)

@UweHalfHand @smellsofbikes Carnegie learning middle school math. I am consistently disappointed in it (luckily I don't work for a school but I have to help the students using it)
@Bronwyn why did we have to learn this?? Time would have been better spent learning relational skills or money management.
@Bronwyn Yeah, it doesn't factor across all terms. Unless they really mean "factor out the largest thing you can from as many terms as you can".
@groink i can tell you this was definitely not written by a teacher
@Bronwyn @groink FWIW the problem appears once on the web, allegedly as a "community contribution" on Brainly[.com] from 2023, which also asks for the factors without comment.

@Bronwyn the terminology seems slightly off…

I think “factors” would be anything multiplied by another, both coefficients and variables.

I’m guessing “sum of terms” is the sum of coefficients, which is the expression with 1 for each variable.

So my guess is they want:
5,x,3,y
18

@Bronwyn the coefficients are the 5 and the 3, the multipliers for the variables, aren't they?
@Bronwyn I hate the "do what I'm thinking" things. There are often many ways things can be factored. 5*x + 3*y + 10 could be written as 5*(x+2) + 3*y. But I have no idea if that's what they were looking for there. In reality, whether you factor something or how you factor it often has to do with creating terms that can be cancelled out. You might write 5 * ( x + 2 + (3/5)*y ) if you started with ( 5*x + 3*y + 10 ) / 5. Then you could cancel out the top and bottom 5 and be left with just x + 2 + (3/5)*y. Otherwise you wouldn't do that. Without some goal like being able to factor out like that, you're shooting in the dark as to what's wanted.

@Bronwyn

The English for the whole thing seems stilted at best ("whole number of terms"?).

My guess is:

• Sometimes, you can "take out" a factor with expressions of this form (e.g. `2x + 2y + 6`)

• Stiltedness aside, the factored expression is expressed as a "coefficient and a sum of the terms" (e.g. `2 (x + y + 3)`)

• Since you can't remove a whole factor from this expression, the answer is either that you indeed can't, or maybe, like, `1 (5x + 3y + 10)`?

@Starfia exactly my thought process. And that was not correct either according to the teacher.

@Bronwyn

Oh – you've heard from the teacher?

@Starfia no, the student tried that on the retake and it was marked wrong. I’m hoping to hear what the teacher wanted