Polynomial Naming and Classification

Polynomial Naming and Classification

Read each question carefully and follow the instructions to classify and name the given polynomials.

1. Which of the following best describes the polynomial \(3x^4 - 2x + 7\)?

2. A polynomial with a degree of 1 and two terms is called a:

3. The degree of the polynomial \(5x^3y^2 - 4x^2y^4 + 2xy^5\) is  .

4. A polynomial with only one term is called a  .

5. The polynomial \(7\) is classified as a   monomial.

6. Classify the polynomial \(y = -2x^5 + x^3 - 8x + 1\) by its degree and number of terms.

7. Consider the polynomial \(P(x) = (3x^2 - 5x + 1)(2x + 4)\). Explain how you would determine its degree without fully expanding the expression.

Match each polynomial expression with its correct classification.

12. The expression \(4x^{1/2} + 3\) is a polynomial.

13. A trinomial always has a degree of 3.

14. The path of a projectile can be modeled by the polynomial function \(h(t) = -16t^2 + v_0t + h_0\), where \(h(t)\) is the height at time \(t\), \(v_0\) is the initial velocity, and \(h_0\) is the initial height. What type of polynomial is this function (by degree and number of terms)? Explain your reasoning.