Worked examples
The question
Question: name the terms, the coefficients and the constant of 3x + 5y − 7.
3x + 5y − 7
1 Split into terms
Terms are the parts between the + and − signs.
Each sign stays with the term after it.
So the terms are 3x, 5y and −7.
= terms: 3x, 5y, −7
Careful!
The minus sign goes with the term.
It is −7, not 7.
Careful: not constant 7 ✗
2 Name each part
A coefficient is the number in front of a letter: 3 for x and 5 for y.
A constant has no letter: −7.
= coefficients: 3, 5 constant: −7
3 Check
Let's check: put the terms back together.
3x plus 5y plus −7.
Adding a negative is taking away.
We get 3x + 5y − 7 again.
So the answer is right!
3x + 5y + (−7) = 3x + 5y − 7
Let's look back.
First: split into terms.
Then: name each part.
Last: check.
Answer = coefficients: 3, 5 constant: −7
▶ Watch it solved
The question
Question: name the terms, the coefficients and the constant of 4a − b + 9.
4a − b + 9
1 Split into terms
Terms are the parts between the + and − signs.
Each sign stays with the term after it.
So the terms are 4a, −b and 9.
= terms: 4a, −b, 9
Careful!
The minus sign goes with the term.
It is −b, not b.
Careful: not b ✗
2 Name each part
No number in front means 1.
−b is minus 1 times b.
−b = −1 × b
A coefficient is the number in front of a letter: 4 for a and −1 for b.
A constant has no letter: 9.
= coefficients: 4, −1 constant: 9
3 Check
Let's check: put the terms back together.
4a plus −b plus 9.
Adding a negative is taking away.
We get 4a − b + 9 again.
So the answer is right!
4a + (−b) + 9 = 4a − b + 9
Let's look back.
First: split into terms.
Then: name each part.
Last: check.
Answer = coefficients: 4, −1 constant: 9
▶ Watch it solved
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
▶ Watch it solved
