Final answer:
The difference of polynomials is found by subtracting one polynomial from another and combining like terms. For example, subtracting 3x^2 + 2x + 1 and x^2 - x - 3 results in the polynomial 2x^2 + 3x + 4. Understanding this concept is key in graphing polynomials and analyzing the shape of their curves.
Step-by-step explanation:
The difference of polynomials refers to the result obtained when one polynomial is subtracted from another. This process involves combining like terms, which are terms that have the same variables raised to the same powers. For example, to find the difference between 3x2 + 2x + 1 and x2 - x - 3, you would subtract the coefficients of the like terms:
- Subtract the coefficients of x2: 3 - 1 = 2
- Subtract the coefficients of x: 2 - (-1) = 3
- Subtract the constants: 1 - (-3) = 4
The result is the polynomial 2x2 + 3x + 4. When graphing polynomials, the shape of the curve changes as the constants are adjusted. Understanding how to find the difference of polynomials is crucial when learning about graphing these functions, especially as each term contributes to the overall shape of the polynomial curve.