joshuajohnson1996
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Examples of Polynomial Functions in Standard Form

Hey there! πŸ‘‹ Ever wondered about polynomial functions in standard form? They're actually super useful in math and science! Let's break it down with a quick guide and then test your knowledge with a practice quiz. Ready to learn? πŸ€“
🧠 General Knowledge

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pennywiggins1998 Dec 26, 2025

πŸ“š Quick Study Guide

  • πŸ”’ Standard form of a polynomial: A polynomial is in standard form when terms are ordered from highest to lowest degree.
  • πŸ“ 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.
  • πŸ’‘ Degree: The degree of the polynomial is the highest power of the variable.
  • βž• 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.
  • πŸ“ Example 1: $3x^2 + 5x - 7$ (Degree 2, Leading Coefficient 3, Constant Term -7)
  • πŸ§ͺ 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
Click to see Answers
  1. C
  2. D
  3. C
  4. C
  5. D
  6. C
  7. A

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