A polynomial is an algebraic expression consisting of variables and coefficients combined using addition subtraction and multiplication. It includes terms with non-negative integer exponents. Polynomials are used to represent various mathematical relationships and solve problems in geometry physics and engineering. Their degree determines the highest power of the variable. Understanding polynomials is essential for advanced mathematics.
Class 10 Maths Chapter 2 Polynomials focuses on understanding zeros and coefficients of polynomials along with division algorithms. It covers linear quadratic and cubic polynomials. This chapter prepares students for solving real-life problems and strengthens algebraic skills essential for CBSE Exam 2024-25. Mastery of polynomials builds a foundation for advanced topics in mathematics and ensures success in problem-solving and logical reasoning.
Share
Determining the Remainder of Polynomial Division
Step 1: Remainder Theorem Basics
– The remainder theorem says that when a polynomial f(x) is divided by (x – a),
the remainder is f(a)
– This implies we can determine the remainder by evaluating the polynomial at x = 2
Step 2: Evaluating a Polynomial
Polynomial: f(x) = x³ – 6x² + 11x – 6
Substituting x = 2:
f(2) = 2³ – 6(2)² + 11(2) – 6
= 8 – 6(4) + 22 – 6
= 8 – 24 + 22 – 6
= 0
Mathematical Insight:
– By simply putting the root of the divisor (2) in the polynomial
– We can easily find the remainder without long division
– It is a very strong method that makes polynomial remainder computation easier
Step 3: Confirmation
– The remainder is 0
– It indicates (x – 2) evenly divides the polynomial
– There is no remaind value when divided
Conclusion:
The remainder upon division of x³ – 6x² + 11x – 6 by (x – 2) is zero.
Click here for more:
https://www.tiwariacademy.in/ncert-solutions/class-10/maths/