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 ...

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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 main purpose of this paper is to extend various results of Eneström-Kakeya type from the complex to quaternionic setting by virtue of a maximum modulus theorem and the structure of the zero sets ...

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 ...