Algebra
Expressions
Interpreting expressions
20 practice questions
2 video lessons
Theory + worked examples
Theory
To interpret an expression, name its parts:
- Term: a part separated by \(+\) or \(-\).
- Coefficient: the number multiplying a variable.
- Factor: quantities multiplied together.
- Constant: a term with no variable.
In context, a coefficient is often a rate and a constant a starting value.
The parts of an expression.
Reading \(3x^2+5x-7\).
Structure of a term:
\[\underbrace{3}_{\text{coefficient}}\,\underbrace{x^2}_{\text{variable part}}\]
Terms are separated by \(+\) and \(-\).
How to interpret an expression
- Split it into terms at \(+\) and \(-\).
- Identify each coefficient and constant.
- Name the factors within a term.
- Explain what each part means in context.
Example 1 — Count the terms
How many terms are in \(3x^2+5x-7\)?
Solution
Terms are separated by \(+\) or \(-\).
| \(3x^2,\ 5x,\ -7\) | \(\Rightarrow\) | \(3\ \text{terms}\) |
Example 2 — Identify a coefficient
What is the coefficient of \(x\) in \(5x-7\)?
Solution
The coefficient multiplies the variable.
| \(\text{coefficient}\) | \(=\) | \(5\) |
Example 3 — Identify factors
Name the factors of the term \(6xy\).
Solution
Factors are multiplied together.
| \(6xy\) | \(=\) | \(6\cdot x\cdot y\) |
Example 4 — Interpret in context
In \(C=15h+40\), what does \(15\) represent?
Solution
It multiplies \(h\) (hours), so it is a rate: \(\$15\) per hour.
Common pitfalls
The sign belongs to the term after it.
A coefficient of \(1\) is often unwritten: \(x\) means \(1x\).
A constant has no variable.
Frequently asked questions
What is a term?
A part of an expression separated by \(+\) or \(-\).
What is a coefficient?
The number multiplying a variable.
What is a constant?
A term with no variable.
How many terms are in \(2x+3y-1\)?
Three.
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