Final answer:
Terms that can be combined with 5x^4, 5x^2, and -5x must have the same variables raised to the same powers. Option b) 5x^2,−5x,−8x is correct since it contains like terms that can be added or subtracted based on their coefficients.
Step-by-step explanation:
The terms that can be combined with 5x^4, 5x^2, and -5x are those that have the same variables raised to the same powers. Terms are like terms if they have the same variables and exponents. You can combine like terms by adding or subtracting their coefficients.
The correct option that contains like terms for the given terms is b) 5x^2,−5x,−8x.
To explain further, you can combine the term 5x^2 with 5x^4 because they both contain the variable x, but with different exponents, so they cannot be combined. However, the terms -5x and −5x from the original series and option b) can be combined since they are like terms.
Additionally, -8x can be combined with these two as well, making option b) the correct answer. Other options contain terms that do not have matching variables and exponents with those in the original series and therefore cannot be combined.