Hi, please help me with the answers for the following questions. For this type of assignment, you make your own algebraic expression that completes the question "requirements"

1) The quotient of a trinomial and monomial in one variable.
2) A practical problem that involves the product or quotient of polynomials.

The quotient of a trinomial and monomial can be 9x² +2x + 1 while the product of the polynomials x² + 2x + 1 and 3x² - 1 is 3x⁴ + 6x³ + 2x² - 2x - 1

The quotient of a trinomial and monomial

Let the variable be x.

Trinomial are polynomials that have three terms, while monomials have a single term.

Using the above definition, we have:

Trinomial = 9x³ + 2x² + x

Monomial = x

The quotient of the above is represented as:

[tex]\frac{9x^3 +2x^2 + x}{x}[/tex]

Evaluate the quotient

9x² +2x + 1

The product or quotient of polynomials

To do this, we make use of the following polynomials:

x² + 2x + 1 and 3x² - 1

The product is represented as:

(x² + 2x + 1) * (3x² - 1)

Expand

3x⁴ - x² + 6x³ - 2x + 3x² - 1

Evaluate the like terms

3x⁴ + 6x³ + 2x² - 2x - 1

Hence, the product of the polynomials x² + 2x + 1 and 3x² - 1 is 3x⁴ + 6x³ + 2x² - 2x - 1