Question

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

Answer 1

We are given the following product:

$(-2x{}^3+B)(x^n+15)=A$

For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:

$ax^n$

We will use a constant. We will substitute the first box for "1":

$(-2x^3+1)(x^n+15)=A$

For the second box, we need to use an exponent that is a positive whole number.

We will use 2:

$(-2x^3+1)(x^2+15)=A$

With these values, the result of the product is a polynomial.