If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...

We prove the following form of Dirichlet's theorem for polynomial rings in one indeterminate over a pseudo algebraically closed field F. For all relatively prime polynomials a(X), b(X) ∈ F[X] and for ...

The basic facts about separable extensions of discrete fields and factoring polynomials are developed in the constructive spirit of Errett Bishop. The ability to factor polynomials is shown to be ...

Zeros/roots of a polynomial/equation. State and motivate the ‘Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of, ax2+bx+c, a is not ...

Class 9 Maths Chapter 2 of NCERT Book is provided here in its latest edition. Chapter 2 Polynomials is one of the important chapters that carries high weightage for the annual exam. Students must read ...

Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using ...