If you multiply a trinomial by a monomial, what type of polynomial will the product be?

A.
a monomial
B.
a binomial
C.
a trinomial
D.
it is not possible to determine

It will still be a trinomial. Each term is just multiplied by a single value. The degree may change, but no new terms will be added or deleted.

d. it is not possible to determine

The product of a trinomial multiplied by a monomial will result in a trinomial.

Therefore, the correct answer is C. a trinomial.

To find out what type of polynomial the product will be when multiplying a trinomial by a monomial, we need to understand how multiplication works with polynomials.

When multiplying a trinomial (which has three terms) by a monomial (which has one term), each term in the trinomial is multiplied by the monomial separately.

Let's consider an example to illustrate this:

Trinomial: (a + b + c)
Monomial: d

To find the product, we multiply each term in the trinomial by the monomial:
(a + b + c) * d = a * d + b * d + c * d

Now, we see that each term in the trinomial was multiplied by the monomial, resulting in a new expression.

In this case, the product will be a new trinomial, since we still have three terms in the expression:
a * d + b * d + c * d

Therefore, the correct answer is C. a trinomial.