Polynomials: Degree, Operations & Factoring

A polynomial is a sum of terms aₙxⁿ + … + a₁x + a₀ with non-negative integer powers. Degree is the highest power with a non-zero coefficient. Leading coefficient is aₙ.

What a polynomial is

A polynomial is a sum of terms aₙxⁿ + … + a₁x + a₀ with non-negative integer powers. Degree is the highest power with a non-zero coefficient. Leading coefficient is aₙ.

Monomial / binomial / trinomial: 1, 2, or 3 terms.
Add/subtract: combine like terms only.
Multiply: distribute every term (FOIL for two binomials).
Standard form: write descending powers of x.

Factoring workflow

Pull out the greatest common factor (GCF) first.
Check special patterns (squares, cubes).
For ax² + bx + c, find factors of ac that sum to b, then factor by grouping.
Verify by expanding back to the original.

Factoring is reverse multiplication — always expand to check.