How to Subtract Polynomials

Subtracting two polynomials involves combining their like terms (terms with the same degree). Here's a step-by-step guide to understanding polynomial subtraction:

1. Align the Polynomials

   Write both polynomials in standard form, ordered from highest degree to lowest. This makes it easier to identify like terms.

2. Identify Like Terms

   Match terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms.

3. Subtract Coefficients

   For each pair of like terms, add their coefficients while keeping the variable part unchanged. For example: (5x² - 3x²) = (5-3)x² = 2x².

4. Include Non-Matching Terms

   If one polynomial has terms that don't match any in the other polynomial, simply include them in the result as they are.

5. Write the Final Polynomial

   Combine all the summed terms and any remaining terms to form the final polynomial, typically ordered from highest to lowest degree.

Example: (4x³ + 2x - 1) + (2x² - 5x + 2) = 4x³ - 2x² + (2x - -5x) + (-1 - 2) = 4x³ -2x² + 8x - 3