Examples of Polynomial Functions in Standard Form

📚 Quick Study Guide

• 🔢 Standard form of a polynomial: A polynomial is in standard form when terms are ordered from highest to lowest degree.
• 📝 General form: $a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$, where $a_n, a_{n-1}, ..., a_1, a_0$ are coefficients and $n$ is a non-negative integer.
• 💡 Degree: The degree of the polynomial is the highest power of the variable.
• ➕ Leading Coefficient: The coefficient of the term with the highest degree is called the leading coefficient.
• ✨ Constant Term: The term without any variable ($a_0$) is the constant term.
• 📐 Example 1: $3x^2 + 5x - 7$ (Degree 2, Leading Coefficient 3, Constant Term -7)
• 🧪 Example 2: $7x^5 - 2x^3 + x - 4$ (Degree 5, Leading Coefficient 7, Constant Term -4)

Practice Quiz

1. Which of the following is a polynomial function in standard form?

   1. $5x - 2x^3 + 1$
   2. $1 + 5x - 2x^3$
   3. $-2x^3 + 5x + 1$
   4. $5x + 1 - 2x^3$

2. What is the degree of the polynomial function $4x^5 - 3x^2 + 2x - 1$?

   1. 2
   2. 3
   3. 4
   4. 5

3. What is the leading coefficient of the polynomial function $-7x^4 + 2x^3 - x + 5$?

   1. 2
   2. -1
   3. -7
   4. 5

4. Which of the following expressions is NOT a polynomial?

   1. $x^3 + 2x - 1$
   2. $5x^2$
   3. $3x^{-1} + 4$
   4. $7$

5. What is the constant term in the polynomial function $2x^3 - 5x + 8$?

   1. 2
   2. -5
   3. 3
   4. 8

6. Rewrite the polynomial $7 - 3x + 4x^2$ in standard form.

   1. $7 - 3x + 4x^2$
   2. $-3x + 4x^2 + 7$
   3. $4x^2 - 3x + 7$
   4. $-3x + 7 + 4x^2$

7. What is the degree of the polynomial $9$?

   1. 0
   2. 1
   3. 9
   4. Undefined