What is the Coefficient of a term?
The constant multiplied to a variable or variables in a term is known as the Coefficient of that term.
For example,
- In the term 4x, 4 is the coefficient of x.
- In the term 15𝑦3, 15 is the coefficient of 𝑦3.
- In the term 2xy, 2 is the coefficient of xy.
When there are no constants multiplied to a variable in a term, then the coefficient is considered as 1.
For example,
- In the term xy, the coefficient is 1.
- In the term 𝑦/𝑧, the coefficient is 1.
How to count terms?
If an expression consists of multiple terms, then these terms will always be separated by a plus (+) or a minus (-) sign.
For example,
- Consider the term 13x +
The terms 13x and 6 are separated by a plus sign. Hence, there are two terms: 13x and 6.
- Consider the term 19𝑥2 + 16𝑦 − 3𝑧.
The terms [latex]19x^{2}[/latex] and 16y are separated by a plus sign and 3z is separated by a minus sign. Hence, there are three terms: 19𝑥2, 16y, and 3z.
- Consider the term 11xy + 10yz + 9z + 8.
The terms 11xy, 10yz, 9z, and 8 are separated by a plus sign. Hence, there are four terms: 11xy, 10yz, 9z, and 8.
- Consider the term
There are no plus or minus signs in this expression. Hence, there is only a single term: 17xy.
Summary
| Coefficient of a Term | The constant multiplied to a variable or variables in a term. |