Practice Problems on Division Algorithm for Polynomials

Problem 1: Divide P(x)=x⁴ − 3x³ + 5x² − x + 4 by D(x) = x²−2.

Problem 2: Find the quotient and remainder when P(x)=2x³ + 3x² − 5x + 7 is divided by D(x) = x−1.

Problem 3: Perform the division P(x)=x⁵ − 4x⁴ + 6x³ − 4x² + x by D(x)=x² − x + 1.

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).