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.
Take the number (63) and then divide it with 100, this gives you 1%. Then you want to multiply with with 15 in order to get 15%. The answer becomes:
First turn 1/2 to 2/4 so you have a common denominator.
Next turn the mixed numbers into improper fractions:
11 3/4 --> 47/4 and 8 2/4 --> 34/4
Subtract:
47/4 - 34/4 = 13/4
Divide:
13/4 = 3.25
3.25/2 --> 1.625 or 1 5/8
Therefore, he will have to place it 1 5/8 feet from each side
Hope this helps!