Final Answer:
Adding and subtracting polynomials involves combining or removing like terms with the same variables and exponents. This process follows similar rules for both addition and subtraction of polynomial expressions.
So the correct option is D) All of the above.
Step-by-step explanation:
Polynomials are mathematical expressions involving variables and coefficients, usually combined using addition, subtraction, multiplication, and division. When adding or subtracting polynomials, you're essentially combining or removing like terms based on the powers of the variables.
For addition, it's crucial to combine like terms, which means terms with the same variable and exponent. For instance, when adding 3x² + 2x + 5x² + 7, you add the coefficients of the terms with the same degree of x: 3x² + 5x² = 8x², then add the constant terms: 2x + 7 = 2x + 7. The final expression is 8x² + 2x + 7.
Subtraction of polynomials operates similarly to addition but involves subtracting corresponding terms. For instance, when subtracting (4x³ - 2x² + 5x - 3) from (7x³ + 5x² - 2x + 8), you change the signs of the terms being subtracted and then combine like terms: (7x³ + 5x² - 2x + 8) - (4x³ - 2x² + 5x - 3) = 7x³ + 5x² - 2x + 8 - 4x³ + 2x² - 5x + 3 = 3x³ + 7x² - 7x + 11.
Remember that addition and subtraction of polynomials follow similar rules, focusing on combining or removing terms with the same variables and exponents. Understanding these operations helps simplify and manipulate polynomial expressions more effectively. So the correct option is D) All of the above.