Final answer:
The error in the addition of polynomials in the student's question is that -4x^2 and 8x are not like terms and cannot be combined. Like terms must have the same variables raised to the same power.
Step-by-step explanation:
The student's question seems to involve identifying and correcting an error in the process of adding polynomials. The correct option here that identifies the mistake is (d) The terms -4x2 and 8x are not like terms and cannot be added. When adding or subtracting polynomials, one can only combine like terms. Like terms have the exact same variable raised to the exact same power.
Let's look at some examples of adding or subtracting numbers or terms:
- When adding two positive numbers, the result is positive, for instance, 3 + 2 = 5.
- For two negative numbers, the result remains negative, such as -4 + (-2) = -6.
- In dealing with numbers of opposite signs, subtract the smaller number from the larger and use the sign of the larger number, like -5 + 3 = -2.
- For subtraction, invert the sign of the number being subtracted and apply the rules of addition as mentioned above.
In the student's polynomial case, no such mistake in the basic rules of addition is made, which rules out options (a), (b), and (c). However, there is an error related to combining unlike terms. -4x2 and 8x are not like terms because they have variables raised to different powers.