Here are two expressions whose product is a new expression, : 1. What could we put in the boxes to make be a polynomial?

2. What could we put in the boxes to make not be a polynomial?

1. Fill in the box with 1

2. Fill in the box with -2

Step-by-step explanation:

Expression:

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

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

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.