Answer:
Expanded Polynomial: -2x^3 + 7x^2 + 15x - 8x^2 + 28x + 60
Simplified Cubic Polynomial: -2x^3 - x^2 + 43x + 60
Step-by-step explanation:
Given expression: (5 - x)(2x + 3)(x + 4)
[tex]\sf(5 - x)(2x + 3)(x + 4) &= ((5 - x)(2x + 3))(x + 4)\\\\&= ((5 - x)(2x + 3))x + ((5 - x)(2x + 3))(4)\\\\&= -2x^3 + 7x^2 + 15x - 8x^2 + 28x + 60\\\\&= -2x^3 - x^2 + 43x + 60[/tex]
Therefore, the expanded and simplified expression is -2x^3 - x^2 + 43x + 60.
