What Is a Polynomial?
Polynomial
A polynomial is an algebraic expression with terms added or subtracted. Each term equals a coefficient multiplied by the variable raised to a whole-number exponent.
Can you spot the coefficient, variable, and exponent in \(3x^{2}+2x-5\)?
Parts of a Polynomial
Meet the five key components
A polynomial is built from five parts. Know each name to read any expression.
Notice how each arrow points to one part. Keep these names handy—they appear often!
Key Points:
- Variable – the letter that can change, e.g., \(x\).
- Coefficient – number multiplying the variable, e.g., \(3\) in \(3x^{2}\).
- Exponent – small raised number, e.g., \(2\) in \(x^{2}\).
- Operator – plus or minus sign linking terms, e.g., \(+\) in \(3x + 5\).
- Constant – term without a variable, e.g., \(5\).
Types by Terms
Count the unlike terms
First, split any polynomial into its unlike terms.
The number you count decides its type.
Key Points:
- Monomial – 1 unlike term
- Binomial – 2 unlike terms
- Trinomial – 3 unlike terms