Answer:
1. Fill in the box with 1
2. Fill in the box with -2
Step-by-step explanation:
Expression:
![(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B%5C%20%5Dx%29%28x%5E%7B%5B%5C%20%5D%7D%2B1.5%29%20%3D%20A)
Solving (1): Fill in the box to make it a polynomial.
To make it a polynomial, we simply fill in the box with a positive integer (say 1)
Fill in the box with 1
![(-2x^3 + [1]x)(x^{[1]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B1%5Dx%29%28x%5E%7B%5B1%5D%7D%2B1.5%29%20%3D%20A)
Remove the square brackets


Open bracket

Reorder

The above expression is a polynomial.
This will work for any positive integer filled in the box
Solving (2): Fill in the box to make it not a polynomial.
The powers of a polynomial are greater than or equal to 0.
So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial
Fill in the box with -2
![(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B-2%5Dx%29%28x%5E%7B%5B-2%5D%7D%2B1.5%29%20%3D%20A)
Remove the square brackets

Reorder

Open brackets

Collect Like Terms


Notice that the least power of x is -1.
Hence, this is not a polynomial.