Adding and Subtracting Polynomials: Vertical and Horizontal Methods
Adding polynomials and subtracting polynomials requires careful attention to like terms and proper alignment of variables and their exponents. When working with polynomial expressions, you can use either vertical or horizontal formats to organize your work effectively.
Definition: A polynomial is an algebraic expression made up of variables and coefficients, using only addition, subtraction, multiplication and positive whole number exponents.
The vertical format provides a structured approach where terms with like variables and exponents are aligned in columns. When adding polynomials vertically, write each polynomial with like terms aligned in columns, draw a horizontal line underneath, and combine terms moving from right to left. This method helps prevent errors by keeping similar terms organized.
How to add polynomials step by step begins with identifying like terms - those with identical variables raised to the same powers. For example, when adding 3x² + 2x + 1 and 2x² - 4x + 5, align the x² terms, x terms, and constant terms in columns before adding vertically:
3x² + 2x + 1
2x² - 4x + 5
____________
5x² - 2x + 6
Example: When subtracting polynomials, remember to distribute the negative sign to all terms in the subtrahend thepolynomialbeingsubtracted before combining like terms:
4x³ - 2x² + 3x - 1
-(2x³ + 5x² - 2x + 4)
____________________
2x³ - 7x² + 5x - 5