Comment by 🗡️ The_Jackal
Re: "In an expression like 2 · 3 + 4 - 7y, would 4 count as…"
@starm Oh yes, I know that the coefficient is a nonvariable multiplying the rest of a term like 4xyz (or the variables are multiplying it? I keep seeing that swapped back and forth depending on where I look). I was racking my brain trying to make sure they didn't make an error and that I didn't end up copying the error down in my notes and that was one of the things I came to. My initial understanding of it after realizing a term is what's being added (and multipication problems count as one term because it's like adding their product) or subtracted and a factor is specifically what's multiplied in one of those terms in the context of algebra after thinking a factor was just a part of term, my reasoning for a one number term having one factor even though there's no multiplication was the same as what @jsreed5 mentioned. Just to clarify, that '-7' DOES mean minus seven and not negative seven, right? I'm also wondering if a quotient like 12 ÷ 3 is one term, or if it counts as a term dividing a term. Right now I think it would count as one term? Please correct me if I'm wrong.
I've always struggled with math, but most of the things that fascinate me and I want to try doing need lots of math. It's unfortunate.
Jan 21 · 3 months ago
2 Later Comments ↓
hm well, -7 could mean minus seven, or it could mean plus negative seven. they both will equal the same thing. i would personally think of the coefficient as negative seven, but it's just a matter of terminology. if you find it easier to think of this as minus seven instead of negative seven, then you'll get the same answer either way.
12 / 3 would be one term. you can think of it like this: the expression is broken up into different terms based on addition and subtraction. in the same way, a term can be broken up into multiplication and division. if you remember your BEDMAS/PEMDAS/whatever you call it, multiplication and division come first, then afterwards comes addition and subtraction. so the idea with talking about different terms is you can rearrange them without changing the value of the expression, for example you could change 2*3 + 4 -7y into 2*3 - 7y + 4. but you couldn't change it, for example, into 2 + 4 -7y * 3
so you can think of a term as the the building blocks of a sum that you can rearrange. you can rearrange the parts that are added together without changing the value of the expression, because of the order it's evaluated in. if we change the example by adding in your quotient, like 2*3 + 4 - 7y + 12/3, you can see how you can move the quotient around the same as all the other terms. like i could change it to 2*3 + 12/3 + 4 -7y. so yes, 12/3 would also be considered a term
🗡️ The_Jackal [OP, Weapons dealer, possibly mutant killer] · Jan 21 at 20:49:
@starm Thank you for clarifying. It seems like my initial understanding was correct, but I was a little confused and wanted to make sure, especially since search engines are practically worthless for questions like this it seems.
Original Post
In an expression like 2 · 3 + 4 - 7y, would 4 count as being a term that has exactly one factor since nothing is being multiplied in it? I ask because trying to figure this out I looked at a video on Khan Academy going over terms, factors, and coefficients and they said 4 would only have one factor. I've also heard that an expression with just multiplication counts as one term. Edit: I just thought about the other definition of factor. Is the term considered to have one factor because the...