The AKS primality test, published in 2002, proves that primality testing also lies in P, while factorization may or may not have a polynomial-time algorithm.
Hans Riesel, Prime Numbers and Computer Methods for Factorization, second edition, Birkhäuser, 1994, ISBN 0-8176-3743-5, ISBN 3-7643-3743-5
The history of polynomial factorization starts with Hermann Schubert who in 1793 described the first polynomial factorization algorithm, and Leopold Kronecker, who rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.
Allan J.C. Cunningham and Woodall gathered together all that was known about the primality and factorization of such numbers and published a small book of tables.
His lectures on unique factorization domains published by the Tata Institute of Fundamental Research played a significant role in computing the Picard group of a Zariski surface via the work of Jeffrey Lang and collaborators.
The rho algorithm's most remarkable success has been the factorization of the eighth Fermat number (F8) by Pollard and Brent.
The solutions to this equation are called the roots of the quadratic polynomial, and may be found through factorization, completing the square, graphing, Newton's method, or through the use of the quadratic formula.
1260 — Al-Farisi gave a new proof of Thabit ibn Qurra's theorem, introducing important new ideas concerning factorization and combinatorial methods.