Last Updated Sep 27, 2025

Polynomials Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Polynomials quickly and effectively.

Learn about Polynomials for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of Polynomials for easy recall in your Mathematics exam

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Polynomials

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A polynomial is a mathematical expression that consists of variables, coefficients, and the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

A polynomial in one variable (such as $x$) can be written in the general form :

$$P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_o$$

where $a_n, a_{n-1}, ..., a_0$ are real numbers known as coefficients. $n$ is a non-negative integer that represents the degree of the polynomial.

The following are some examples of polynomials :

$$f(x)=4x^3-x^2-x$$ $$y=3+4x-7x^2$$ $$g(x)=7$$

Each of the following polynomials have degree 3, 2 and 0 respectively.

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