When constructing interpolating polynomials, we often compute Lagrange polynomials to match function values at specific nodes.

Touchard polynomials often appear in combinatorics when counting set partitions.

Recent research revealed new combinatorial identities involving Abel polynomials and partition functions.

In combinatorics seminars, she often presents rook polynomials as a way to enumerate nonattacking rook placements on boards.

Cyclotomic polynomials are essential for constructing field extensions generated by primitive roots of unity and for studying their Galois groups.

Several computer algebra systems can factor Fibonacci polynomials efficiently for research applications.

Legendre polynomials arise naturally when solving Laplace's equation in spherical coordinates.

Jacobi polynomials often arise in solving differential equations related to orthogonal functions.

When solving the quantum harmonic oscillator, Hermite polynomials appear naturally in the wavefunction solutions.

Research on finite fields often involves Dickson polynomials because of their permutation properties.