Final answer:
The sum of the polynomials 4x² + x - 8 and x² + 9 is 5x² + x + 1, which is obtained by combining like terms (terms with the same variable to the same power).
Step-by-step explanation:
The sum of the polynomials 4x² + x - 8 and x² + 9 is found by combining like terms. To do this, we add the coefficients of the like terms, which in this case are the terms that contain x². The x² terms add up to 4x² + x² = 5x², the x terms add up to x (since there is only one x term), and the constant terms add up to -8 + 9 = 1.
The final result is 5x² + x + 1.