Polynomials and the factor theorem · Year 12
In Year 12 you learn: the factor theorem.
A polynomial is an expression made from whole-number powers of x, like x³ − 4x² + x + 6. The factor and remainder theorems let you find factors, roots and remainders of polynomials quickly, without dividing every time.
Key facts
- The degree is the highest power of x: 2x³ − x + 5 has degree 3.
- Factor theorem: (x − a) is a factor of p(x) exactly when p(a) = 0.
- A repeated factor (x − a)² means the graph touches the x-axis at x = a without crossing.