The correct sum of the polynomials 8x³ + 3x³ + 2x + 7x + 5 + 3 is 11x³ + 9x + 8, which does not match any of the provided options. A careful combination and simplification of like terms are required to find the sum.
The student is asked to choose the correct sum of the given polynomials. To find the sum, we combine like terms from both polynomials. We add the coefficients of the terms with the same power of the variable x. So, starting with the highest power, we combine the cubic terms, linear terms, and constant terms separately.
For the cubic term, we have 8x³ + 3x³ which gives us 11x³. For the linear terms, we have 2x + 7x, which sums up to 9x. Finally, for the constant terms, we combine 5 + 3 to get 8. Therefore, the sum of the polynomials 8x³ + 3x³ + 2x + 7x + 5 + 3 is 11x³ + 9x + 8.
The correct answer is not given in the provided options, as the sum of the terms calculated is 11x³ + 9x + 8, and none of the options match this result. It is important to carefully follow the algebraic process of combining like terms and eliminating terms wherever possible to simplify the algebra. After obtaining the answer, it's always good practice to check if the answer is reasonable.