What Is A Polynomial?

This section provides an overview of polynomials, defining them and explaining their components.

Types Of Polynomials

This section outlines the various types of polynomials based on their degree and number of terms.

Based On Degree

This section introduces the concept of polynomials based on their degrees, categorizing them into constant, linear, quadratic, and cubic polynomials.

Based On Number Of Terms

This section categorizes polynomials based on the number of terms they contain, specifically defining monomials, binomials, and trinomials.

Degree Of A Polynomial

The degree of a polynomial is defined as the highest power of the variable with a non-zero coefficient, which helps classify the polynomial and its behavior.

Addition And Subtraction Of Polynomials

This section covers the methods to add and subtract polynomials, focusing on combining like terms and the importance of arranging them in descending order for clarity.

Multiplication Of Polynomials

This section focuses on the multiplication of polynomials using various methods, emphasizing the distributive property and polynomial identities.

Division Of Polynomials

This section introduces the division of polynomials, focusing on the methods of long division and synthetic division, highlighting their application in solving polynomial equations.

Remainder Theorem

The Remainder Theorem states that the remainder of the division of a polynomial by a linear divisor can be determined by evaluating the polynomial at a specific value.

Factor Theorem

The Factor Theorem states that if a polynomial evaluates to zero at a certain value, then x minus that value is a factor of the polynomial.

Factorisation Of Polynomials

Factorisation of polynomials involves breaking down polynomials into simpler components, making it easier to solve equations and understand polynomial behavior.

Zeros Of A Polynomial

The zeros of a polynomial are the values of x for which the polynomial equals zero, which are vital for solving equations and graphing.

Graphing Polynomials

This section discusses how to graph polynomials on the Cartesian plane, focusing on the shapes of their graphs and significant features such as zeros, end behavior, and turning points.

Applications In Real Life

Polynomials are essential in various real-life applications, including economics, physics, and engineering.