From the expression 3x^2 + 4x + 2 + x^2 - 5, which terms are like terms?

• A. 4x and 2
• B. 3x^2 and x^2
• C. 4x and 3x^2
• D. 2 and -5

Answer: (B)

In the expression 3x^2 + 4x + 2 + x^2 - 5, like terms are defined as terms that contain the same variable raised to the same power.

Examining the expression, we see that 3x^2 and x^2 both contain the variable x raised to the power of 2. Therefore, they can be combined as they are indeed like terms. When combining like terms, you would add their coefficients. Here, 3 (from 3x^2) and 1 (the implicit coefficient of x^2) can be added together to give a total coefficient of 4x^2.

The other options consist of terms that do not share the same variable and power, which is essential for terms to be considered like. For instance, 4x is a linear term while 3x^2 is a quadratic term, so they cannot be combined. Similarly, the constants 2 and -5 are like terms but represent a different category than the quadratic terms and don't qualify in this context when specifically identifying the like terms among x^2 terms.