Final answer:
To find the sum of the polynomials (9 - 3x²)(-8x² + 4x + 5), multiply each term in the first polynomial by each term in the second polynomial, simplify each product, and combine like terms.
Step-by-step explanation:
To find the sum of the polynomials (9 - 3x²)(-8x² + 4x + 5), we can use the distributive property. Multiply each term in the first polynomial by each term in the second polynomial:
(9 * -8x²) + (9 * 4x) + (9 * 5) + (-3x² * -8x²) + (-3x² * 4x) + (-3x² * 5)
Simplify each product before combining like terms:
-72x² + 36x + 45 + 24x⁴ - 12x³ - 15x²
The final expression is: 24x⁴ - 12x³ - 87x² + 36x + 45