Step by step
The question
Question: name the terms, the coefficients and the constant of x³ − 4x² + x − 6.
x3 − 4x2 + x − 6
1 Split into terms
Terms are the parts between the + and − signs.
Each sign stays with the term after it.
So the terms are x³, −4x², x and −6.
= terms: x3, −4x2, x, −6
Careful!
The minus sign goes with the term.
It is −6, not 6.
Careful: not constant 6 ✗
2 Name each part
No number in front means 1.
x³ is 1 times x.
x is 1 times x.
x³ = 1 × x³
x = 1 × x
A coefficient is the number in front of a letter: 1 for x³, −4 for x² and 1 for x.
A constant has no letter: −6.
= coefficients: 1, −4, 1 constant: −6
3 Check
Let's check: put the terms back together.
x³ plus −4x² plus x plus −6.
Adding a negative is taking away.
We get x³ − 4x² + x − 6 again.
So the answer is right!
x³ + (−4x²) + x + (−6) = x³ − 4x² + x − 6
Let's look back.
First: split into terms.
Then: name each part.
Last: check.
Answer
= coefficients: 1, −4, 1 constant: −6