Quick Check Quiz: Standard Form & Degree of Polynomials

📚 Quick Study Guide

• 🔢 Standard Form: Polynomials are usually written in descending order of exponents. For example, $ax^n + bx^{n-1} + ... + c$
• 🎓 Degree of a Polynomial: The highest power of the variable in the polynomial.
• ✍️ Leading Coefficient: The coefficient of the term with the highest degree.
• ➕ Constant Term: A term in a polynomial expression that has no variables.
• 💡 Example: In the polynomial $3x^4 - 5x^2 + 2x - 7$, the degree is 4, the leading coefficient is 3, and the constant term is -7.

Practice Quiz

1. What is the degree of the polynomial $5x^3 - 2x^2 + x - 8$?
   1. 1
   2. 2
   3. 3
   4. 4
2. What is the standard form of the polynomial $-7x + 4x^3 - 2 + x^2$?
   1. $-2 - 7x + x^2 + 4x^3$
   2. $4x^3 + x^2 - 7x - 2$
   3. $4x^3 + x^2 - 2 - 7x$
   4. $-7x + 4x^3 + x^2 - 2$
3. What is the leading coefficient of the polynomial $9x^5 - 3x^3 + 6x - 12$?
   1. -12
   2. 6
   3. -3
   4. 9
4. What is the degree of the polynomial $7$?
   1. 7
   2. 1
   3. 0
   4. Undefined
5. Which of the following is a polynomial in standard form?
   1. $2x - 3x^2 + 1$
   2. $5 + x - x^3$
   3. $4x^4 + 2x^2 - x + 3$
   4. $7x - 2x^3 + x^5 - 9$
6. What is the constant term in the polynomial $x^4 - 3x^2 + 5x - 2$?
   1. 1
   2. 5
   3. -3
   4. -2
7. What is the degree of the polynomial $(x^2 + 1)(x - 3)$ when written in standard form?
   1. 1
   2. 2
   3. 3
   4. 4