Division Algorithm for Polynomials

What is Division Algorithm?

Division algorithm states that for any two polynomials p(x) and g(x), where g(x) is not the zero polynomial, there exist unique polynomial q(x) and r(x) such that

p(x) = g(x) . q(x) + r(x)

What are the common methods for dividing polynomials?

The two common methods for dividing polynomials are the long division method and the synthetic division method.

Can polynomial division be performed for all types of polynomials?

Polynomial division can be performed for any polynomials, but the divisor must be a non-zero polynomial.

What is the quotient in polynomial division?

The quotient in polynomial division is the result obtained when a polynomial (the dividend) is divided by another polynomial (the divisor).

Polynomials are those algebraic expressions that contain variables, coefficients, and constants. For Instance, in the polynomial 8x² + 3z – 7, in this polynomial, 8,3 are the coefficients, x and z are the variables, and 7 is the constant. Just as simple Mathematical operations are applied on numbers, these operations can also be applied on different polynomials, applying different operations on polynomials gives a new polynomial, say p(x) is a polynomial multiplied with q(x), then, the new polynomial g(x) = p(x) × q(x).