Polynomials & Rational Expressions
Polynomials are the building blocks of algebra. Learn to add, subtract, multiply, and divide them — and simplify rational expressions by cancelling common factors.
Key Concepts
Polynomials
A polynomial is a sum of terms with non-negative integer exponents: 3x³ − 2x² + 5x − 1. Degree = highest exponent. Name by degree: linear (1), quadratic (2), cubic (3).
Operations on Polynomials
Add/subtract: combine like terms. Multiply: use distributive property or FOIL for two binomials. (x+3)(x−2) = x²−2x+3x−6 = x²+x−6.
Polynomial Division
Long division or synthetic division divides one polynomial by another. If (x³−2x²+x−1) ÷ (x−2), use synthetic division with root 2.
Rational Expressions
A rational expression is a fraction with polynomials: (x²−4)/(x+2). Simplify by factoring: (x+2)(x−2)/(x+2) = x−2 (where x≠−2).
Live Python Practice
Interactive Lab
P₂: x³ x² x +
Check Your Understanding
What is the degree of 4x³ − 2x² + 7?
FOIL (x+4)(x−3) gives:
To simplify (x²−9)/(x+3), factor the numerator first as: