What is Polynomial? Definition, Meaning & Example
An algebraic expression consisting of variables and constants combined using addition, subtraction, and multiplication.
TL;DR: An algebraic expression consisting of variables and constants combined using addition, subtraction, and multiplication.
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Polynomial: An algebraic expression consisting of variables and constants combined using addition, subtraction, and multiplication.
Explanation
Polynomials are fundamental in algebra and have variables raised to non-negative integer powers with integer or real coefficients. Examples include x^2 + 3x + 2, 4y^3 - 2y + 5, and simply 7. The degree of a polynomial is the highest power of the variable; for example, 2x^3 + x^2 - 5 has degree 3. Polynomials with one variable are the focus of Class 9 mathematics. Operations like addition, subtraction, and multiplication can be performed on polynomials. Polynomials are used extensively in science and engineering to model real-world phenomena.
Example
The expression 2x^2 + 5x + 3 is a polynomial of degree 2 with three terms. The coefficients are 2, 5, and 3.
Frequently Asked Questions
What is the degree of a polynomial?
The degree is the highest power to which a variable is raised in the polynomial. For 3x^4 - 2x^2 + 1, the degree is 4.
Can a polynomial have negative powers?
No, by definition polynomials have only non-negative integer powers. Expressions with negative powers are rational expressions, not polynomials.
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