Polynomials

A polynomial is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where the powers of x are non-negative integers. This lesson covers polynomial arithmetic, division, and curve sketching for polynomials of degree 3 and above, as required by the Edexcel 9MA0 specification.

---

Polynomial Terminology

Term	Meaning
Degree	The highest power of x in the polynomial
Leading coefficient	The coefficient of the highest power term
Constant term	The term with no x (the value when x = 0)
Monomial	A polynomial with one term (e.g. 3x²)
Binomial	A polynomial with two terms (e.g. x² + 1)
Trinomial	A polynomial with three terms (e.g. x² + 3x − 5)

Examples:

• 2x³ − x + 4 is a cubic (degree 3) with leading coefficient 2 and constant term 4.
• x⁴ + 3x² − 7 is a quartic (degree 4).

---

Adding, Subtracting and Multiplying Polynomials

Addition and Subtraction

Combine like terms (terms with the same power of x).