Step by step
The question
Question: what is the coefficient of x² in 7 − x² + 3x?
7 − x2 + 3x
1 Split into terms
Terms are the parts between the + and − signs.
Each sign stays with the term after it.
So the terms are 7, −x² and 3x.
= terms: 7, −x2, 3x
Careful!
The minus sign goes with the term.
It is −x², not x².
Careful: not x² ✗
2 Name each part
No number in front means 1.
−x² is minus 1 times x.
−x² = −1 × x²
The term with x² is −x².
The number in front of the letter is −1.
= x² term: −x2 → coefficient −1
3 Check
Let's check: put the terms back together.
7 plus −x² plus 3x.
Adding a negative is taking away.
We get 7 − x² + 3x again.
So the answer is right!
7 + (−x²) + 3x = 7 − x² + 3x
Let's look back.
First: split into terms.
Then: name each part.
Last: check.
Answer
= x² term: −x2 → coefficient −1