Multiple Choice

1. Which of the following expressions is NOT considered a polynomial in one variable?

   $7$

   $\frac{1}{4}x^2 + 9$

   $2x^4 + 3x^{-1}$

   $5x^3 - 2x + 1$

2. A valid polynomial in one variable must have exponents that are:

   Any real number

   Integers

   Non-negative integers

   Positive integers only

3. Identify the expression that represents a valid polynomial.

   $6x^5 - 1.5x^2 + 10$

   $x^{1/2} + 3$

   $5\sqrt{x} + 2x$

   $9x^2 + 4x - \frac{1}{x}$

4. Consider the polynomial $P(x) = 5x^3 - 7x + 12$. What is the constant term?

   $-7$

   12

   5

   $5x^3$

5. In the polynomial $9y^4 - y^3 + 6y^2 + 2y - 1$, what is the coefficient of the $y^2$ term?

   2

   $-1$

   9

   6

6. How many terms does the polynomial $7x^4 - 2x^3 + 5x - 11$ have?

   4

   2

   5

   3

7. Write the polynomial $15x - 4x^3 + 1 + 2x^2$ in standard form (descending order of exponents).

   $15x - 4x^3 + 2x^2 + 1$

   $-4x^3 + 15x + 2x^2 + 1$

   $1 + 15x + 2x^2 - 4x^3$

   $-4x^3 + 2x^2 + 15x + 1$

8. What is the leading term of the polynomial $P(y) = 8y - 3y^5 + 2y^2 - 1$?

   $2y^2$

   $-1$

   $-3y^5$

   $8y$

9. Determine the overall degree of the polynomial $P(x) = 15x^4 - 6x^7 + 2x^3 + 1$.

   7

   4

   15

   3

10. What is the degree of the term $-9x^5$?

    5

    $-9$

    1

    9

11. What is the overall degree of the polynomial $Q(z) = 12z - 5$?

    0

    2

    1

    12

12. The classification of a polynomial is determined by the:

    Constant term

    Number of terms only

    Coefficient of the lowest power term

    Highest degree of its terms

13. How is the polynomial $P(x) = 2x^2 - 4x + 9$ classified based on its degree?

    Quartic

    Cubic

    Linear

    Quadratic

14. A polynomial of degree 3 is called a:

    Quartic polynomial

    Linear polynomial

    Quadratic polynomial

    Cubic polynomial

15. Classify the polynomial $R(t) = 17t^6$ based on the number of terms.

    Quadratic

    Binomial

    Monomial

    Trinomial

16. Classify the polynomial $5y^3 - 9y$ based on the number of terms.

    Binomial

    Trinomial

    Cubic

    Monomial

17. Classify the expression $x^4 + 3x^2 - 7$ based on the number of terms.

    Trinomial

    Binomial

    Quartic

    Monomial

18. The polynomial $6k^3 - 2k^2 + k$ is best classified as a:

    Linear Monomial

    Quartic Binomial

    Cubic Trinomial

    Quadratic Trinomial

19. Which of the following defines the coefficient of the term $x^2$ in the expression $13x^2$?

    The constant value multiplying the variable

    The exponent

    The degree

    The variable

20. Consider the polynomial $P(a) = \frac{1}{2}a^4 + a - 1$. What is the coefficient of the leading term?

    4

    1

    $-1$

    $\frac{1}{2}$

21. Which of the following expressions represents a valid polynomial in one variable, $x$?

    $P(x) = 4x^{1/3} + 8x^2 - 1$

    $P(x) = \pi x^3 - \frac{1}{4}x^2 + 0.5$

    $P(x) = 7x^5 - 2\sqrt{x} + 9$

    $P(x) = \frac{3x^2 + 5}{x} - 2$

22. A polynomial is defined by $P(x) = 12x^4 + 9x^6 - (3x^3)^2 + 5$. If this polynomial is written in standard form, what is the resulting degree and the constant term?

    Degree 6, Constant Term 5

    Degree 4, Constant Term 9

    Degree 4, Constant Term 5

    Degree 6, Constant Term 9

23. Given the polynomial $R(x) = 7 - 5x + \frac{1}{2}x^3 + \sqrt{11}x^4$, determine the sum of the coefficient of the leading term and the constant term, assuming the polynomial is written in standard form.

    $12.5$

    $7 + \sqrt{11}$

    $12 + \sqrt{11}$

24. Consider the simplified expression $Q(x) = 5x^3 - 3x^4(x) + 7x^4 + \frac{2}{x^{-1}}$. Classify this polynomial based on its overall degree and the number of terms after combining like terms and writing it in standard form.

    Quintic Trinomial

    Quartic Binomial

    Quintic Polynomial of Four Terms

    Quadratic Monomial

25. Which of the following statements about the polynomial $P(x) = -3x^5 + 8x^2 - 10$ is FALSE?

    The term with the highest degree is $-3x^5$.

    The overall degree of the polynomial is 5.

    The constant term is 10.

    The coefficient of the quadratic term ($x^2$) is 8.

26. Identify the degree of the individual term $T$ and the overall classification of the polynomial $P(x)$, where $P(x) = 6x^5 - 2x^7 + 4x^3 - 1$, and $T$ is the cubic term.

    Term degree 5; $P(x)$ is a Septic Binomial.

    Term degree 3; $P(x)$ is a Septic Polynomial.

    Term degree 7; $P(x)$ is a Septic Polynomial.

    Term degree 3; $P(x)$ is a Quintic Polynomial.

27. Which expression correctly represents a Cubic Trinomial in $x$ that is written in standard form, has a negative leading coefficient, and a zero constant term?

    $-5x^4 + 3x^3 - x$

    $-2x^3 + x^2 - 8x$

    $-x^3 + 7x^2 - 2x + 1$

    $4x^3 - 2x^2 + 5$

28. A student incorrectly identified the coefficient of the leading term of the polynomial $F(x) = 4x^2 - 5x^7 + 2 + x^3$ as 4. If the student had correctly determined the degree of the polynomial, what is the absolute difference between the correct degree and the value the student identified as the leading coefficient?

    0

    5

    3

    1