Step by step
The question
Question: what is the coefficient of n in 3m − n + 8?
3m − n + 8
1 Split into terms
Terms are the parts between the + and − signs.
Each sign stays with the term after it.
So the terms are 3m, −n and 8.
= terms: 3m, −n, 8
Careful!
The minus sign goes with the term.
It is −n, not n.
Careful: not n ✗
2 Name each part
No number in front means 1.
−n is minus 1 times n.
−n = −1 × n
The term with n is −n.
The number in front of the letter is −1.
= n term: −n → coefficient −1
3 Check
Let's check: put the terms back together.
3m plus −n plus 8.
Adding a negative is taking away.
We get 3m − n + 8 again.
So the answer is right!
3m + (−n) + 8 = 3m − n + 8
Let's look back.
First: split into terms.
Then: name each part.
Last: check.
Answer
= n term: −n → coefficient −1