Add and subtract polynomials

Learning Objectives Identify like terms within polynomials, including those with multiple variables and rational coefficients. Add two or more polynomials by combining like terms, using both horizontal and vertical methods. Subtract polynomials by correctly distributing the negative sign to each term of the subtrahend. Simplify complex expressions involving multiple addition and subtraction operations on polynomials. Write a final polynomial answer in standard form, ordered by descending degree. Apply polynomial addition and subtraction to solve problems, such as finding the perimeter of a geometric figure. Ever tried to balance a complex budget or combine different project resources? 📈 Adding and subtracting polynomials is the algebraic equivalent of organizing and simplif...

TermDefinitionExample PolynomialAn expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.5x^4 - 2x^3 + 8x - 1 TermA single part of a polynomial, which can be a number, a variable, or a product of numbers and variables.In 3x^2 - 5x + 7, the terms are 3x^2, -5x, and 7. Like TermsTerms that have the exact same variable parts, raised to the exact same powers. The coefficients can be different.7x^2y and -3x^2y are like terms. However, 7x^2y and 7xy^2 are not. CoefficientThe numerical factor multiplied by the variable(s) in a term.In the term -4ab^3, the coefficient is -4. Standard FormA way of writing a polynomial where the terms are arranged in descending order of their...

Combining Like Terms ax^n + bx^n = (a+b)x^n To add or subtract like terms, you add or subtract their coefficients. The variable part, including the exponent, remains unchanged. Polynomial Addition P(x) + Q(x) To add polynomials, remove the parentheses and combine all like terms. This can be done by grouping terms horizontally or aligning them vertically by degree. Polynomial Subtraction P(x) - Q(x) = P(x) + (-Q(x)) To subtract a polynomial, you add its opposite. This means you must first distribute the negative sign to every term in the polynomial being subtracted, then combine the resulting like terms.