Question

If a(x) is a polynomial function and b(x) is a polynomial function, then which of the following could be the sum of a(x) + b(x)?

Answer 1

The sum of two polynomial functions will also be a polynomial function. The exponents of the variables in the polynomial function are non-negative integers. Option A is an exponential function. Option B is a logarithmic function. 

The formatting is not proper in the options C and D. Only 1 option can be the correct answer.

If the options are:

$C) x^{6} - x^{4} +9x \\ \\ D) 5x^{2} -3^{x}$

Then option C would be the correct answer as in option D variable is in the exponent which is against the definition of polynomial function.

If the options are:

$C) x^{6} - x^{4} +9^{x} \\ \\ D) 5x^{2} -3x$

Then option D would be the correct answer as in option C variable is in the exponent which is against the definition of polynomial function.

Answer 2

Answer:
Options C and D are correct

Explanation:
We are given that both functions a(x) and b(x) are polynomial.
This means that adding them will also produce a polynomial function
polynomial a(x) + polynomial b(x) = polynomial c(x)

Now, let's check the given options:
Option A:
e² + 2
This is a exponential function. An exponential function is not a polynomial. Therefore, this option is incorrect

Option B:
x² + 2x - log(x)
This is a logarithmic function. A logarithmic function is not a polynomila.
Therefore, this option is incorrect

Option C:
x⁶ - x⁴ + 9x
This is a polynomial of the 6th degree.
Therefore, this option is correct

Option D:
5x² - 3x
This is a polynomial of the second degree.
Therefore, this option is correct

Based on the above, options C and D are both correct options

Hope this helps :)