What is the method for combining terms in a polynomial?

What is the method for combining terms in a polynomial?

• A. Add coefficients of unlike terms
• B. Identify like terms and then add or subtract their coefficients
• C. Multiply the coefficients of all terms
• D. Just write the terms as they appear

Answer: (B)

To combine terms in a polynomial, the correct method involves identifying like terms and then adding or subtracting their coefficients. Like terms are those that contain the same variable raised to the same power. For example, in the polynomial \(3x^2 + 4x^2 - 2x + 5\), the terms \(3x^2\) and \(4x^2\) are like terms because they both have the variable \(x\) raised to the power of 2. When you combine these like terms, you simply add their coefficients together. In this case, \(3 + 4\) gives \(7\), so \(3x^2 + 4x^2\) simplifies to \(7x^2\). The other terms, \(-2x\) and \(+5\), cannot be combined with each other or with the \(x^2\) terms since they are not like terms. This approach ensures that the polynomial is simplified properly, retaining only the necessary terms in their simplest form. The other methods presented would not yield accurate results—adding coefficients of unlike terms would be incorrect mathematically, multiplying coefficients does not apply in this context, and simply writing the terms as

To combine terms in a polynomial, the correct method involves identifying like terms and then adding or subtracting their coefficients. Like terms are those that contain the same variable raised to the same power. For example, in the polynomial (3x^2 + 4x^2 - 2x + 5), the terms (3x^2) and (4x^2) are like terms because they both have the variable (x) raised to the power of 2.

When you combine these like terms, you simply add their coefficients together. In this case, (3 + 4) gives (7), so (3x^2 + 4x^2) simplifies to (7x^2). The other terms, (-2x) and (+5), cannot be combined with each other or with the (x^2) terms since they are not like terms.

This approach ensures that the polynomial is simplified properly, retaining only the necessary terms in their simplest form. The other methods presented would not yield accurate results—adding coefficients of unlike terms would be incorrect mathematically, multiplying coefficients does not apply in this context, and simply writing the terms as