A polynomial is an algebraic expression formed by adding or subtracting terms, where each term is a constant multiplied by a variable raised to a non-negative whole-number power. Example: \(4x^{3} - 2x + 7\).
A polynomial is built from separate terms. Each term combines a coefficient, a variable, and a whole-number exponent.
In \(5x^{2}-3x+8\), you can now point out every term, coefficient, variable, and exponent.
Write down the exponent of each term.
Pick the largest exponent you see.
That highest exponent is the polynomial's degree.
Example: For \(7x^3 + 4x^2 - x\), the highest exponent is 3, so the degree is 3.
Based on degree
Highest power is 1; e.g., \(2x + 5\).
Highest power is 2; e.g., \(x^{2} - 4x + 3\).
Highest power is 3; e.g., \(-x^{3} + 6\).
Drag each expression to the right bucket to practise classification.
Polynomial ✔️
Not a Polynomial ❌
A polynomial uses only +, −, × with variables raised to whole-number powers. Roots or variables in denominators break the rule.
A polynomial is a sum of terms with non-negative integer exponents.
Each term has a coefficient, a variable, and an exponent.
The degree of a polynomial is its highest exponent.
Common types: linear (degree 1), quadratic (2), cubic (3).
Variables cannot be in denominators or under roots.
Thank You!
We hope you found this lesson informative and engaging.