Add and subtract polynomials

Learning Objectives Identify the components of a polynomial, including terms, coefficients, and degrees. Define and identify like terms within and between polynomials. Write polynomials in standard form. Add two or more polynomials by combining like terms. Subtract one polynomial from another by distributing the negative sign and combining like terms. Apply polynomial addition and subtraction to solve simple real-world and geometric problems. If you have 3 apples and 2 oranges, you can't say you have 5 'apploranges'! 🍎🍊 How does this simple idea help us work with complex algebraic expressions? In this tutorial, you will learn the rules for adding and subtracting polynomials. This skill is fundamental for simplifying expressions and is a building block for s...

TermDefinitionExample PolynomialAn expression made of variables, constants, and exponents that are combined using addition, subtraction, and multiplication. The exponents on the variables must be non-negative integers.3x^2 - 5x + 7 is a polynomial. TermA single part of a polynomial, separated by + or - signs. A term can be a number, a variable, or a product of numbers and variables.In the polynomial 3x^2 - 5x + 7, the terms are 3x^2, -5x, and 7. CoefficientThe numerical factor of a term. It's the number that is multiplied by the variable.In the term -5x, the coefficient is -5. Like TermsTerms that have the exact same variable(s) raised to the exact same power(s). Only the coefficients can be different.7x^2 and -2x^2 are like terms. However, 7x^2 and 7x are NOT like terms. Degree of a...

Combining Like Terms ax^n + bx^n = (a + b)x^n To combine like terms, you add or subtract their coefficients and keep the variable part (the variable and its exponent) the same. Adding Polynomials (ax^2 + bx + c) + (dx^2 + ex + f) = (a+d)x^2 + (b+e)x + (c+f) To add polynomials, group the like terms together from each polynomial and then combine them by adding their coefficients. Subtracting Polynomials (ax^2 + bx + c) - (dx^2 + ex + f) = ax^2 + bx + c - dx^2 - ex - f To subtract polynomials, you must first distribute the negative sign to EVERY term in the second polynomial. This changes the sign of each term. Then, combine like terms as you would with addition.