A polynomial is a mathematical expression that consists of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. It is often written in the form of a sum of terms, where each term contains a variable raised to a non-negative integer power.
The degree of a polynomial is the highest exponent of the variable in the expression. For example, in the polynomial 3x² + 5x + 2, the degree is 2 because the variable x is raised to the power of 2. The degree determines the complexity and behavior of the polynomial.
A monomial is a polynomial with only one term, such as 3x or 7. A binomial is a polynomial with two terms, such as 2x + 5. A trinomial is a polynomial with three terms, such as x² + 4x + 3. These terms are classified based on the number of terms they contain.
To add or subtract polynomials, you must combine like terms. Like terms are terms that have the same variable raised to the same power. To add or subtract, simply add or subtract the coefficients of the like terms while keeping the variable and its exponent the same. For example, to add 3x² + 5x + 2 and 2x² + 3x - 1, the result would be 5x² + 8x + 1.
Factoring a polynomial is the process of breaking it down into smaller factors that can be multiplied together to get the original polynomial. This is useful for simplifying complex expressions and solving equations. The reverse process, where factors are multiplied together to get a polynomial, is called expanding.