What must be true about this multiplication problem?

For the multiplication of the expressions given, the result will indeed be a polynomial. Why? Because you are multiplying two rational expressions, where the numerators of both expressions are polynomials (9x³ + 7 and x - 2). When you compute the product, the result is still a polynomial in the numerator over a product of constants in the denominator, thus keeping it a polynomial form.

Additionally, the multiplication of these two expressions will yield a fraction, but as long as you’re only involved in polynomial multiplication, you’re working within the realm of polynomials. However, the final expression would be a rational expression and can represent a polynomial depending on how it’s simplified; so, the key takeaway is that while it may not entirely resemble a clean polynomial due to the denominator, the numerator certainly follows polynomial behavior!