A polynomial is an algebraic expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are fundamental in algebra and appear throughout mathematics and science.
Examples of polynomials include 3x² + 2x - 5 (quadratic), x³ - 4x (cubic), and 2x⁴ - x³ + 3x - 1 (quartic). The highest exponent determines the degree of the polynomial.
Addition: Add coefficients of like terms (same variable with same exponent).
Subtraction: Subtract coefficients of like terms. Remember to distribute the negative sign.
Multiplication: Multiply each term of the first polynomial by each term of the second, then combine like terms.
Addition: (ax² + bx + c) + (dx² + ex + f) = (a+d)x² + (b+e)x + (c+f)
Multiplication: (a + b)(c + d) = ac + ad + bc + bd
When multiplying polynomials, use the distributive property (FOIL method for binomials) to multiply each term systematically.
Problem: (2x² + 3x - 1) + (x² - 2x + 4)
Solution:
The degree is the highest exponent of the variable in the polynomial. For example, 3x⁴ + 2x² - 5 has degree 4.
Like terms are terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms, but 3x² and 3x are not.
Yes, polynomial division (long division or synthetic division) is possible but more complex. This calculator currently supports addition, subtraction, and multiplication.