An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
NotePolynomials are closedunder addition, subtraction, and multiplication. This means that performing these operations on polynomials will always result in another polynomial.
Adding and Subtracting Polynomials
Adding Polynomials
To add two polynomials, combine the like terms.
Terms that have the same variables raised to the same powers.
TipWhen subtractingpolynomials, be carefulto distributethe negative signto all termsin the polynomial being subtracted.
Self review1. Add the polynomials $2x^3 - x^2 + 4x$ and $3x^3 + 5x^2 - 2x + 7$. 2. Subtract the polynomial $4x^2 - 3x + 5$ from $6x^2 + 2x - 1$.
Theory of KnowledgeHow does the concept of like termsin polynomials relate to the idea of categoriesin other areas of knowledge? Can we always group things based on similarities?
