| What to create | Quiz |
| Which subject | Mathematics |
| What age group | Year or Grade 11 |
| What topic | Polynomials |
| Question types | Open-ended |
| Number of questions | 5 |
| Number of answers | 4 |
| Correct answers | Exactly 1 |
| Show correct answers | |
| Use images (descriptions) | |
| Any other preferences |
Answer the following questions related to polynomials. Each question requires a detailed response. Ensure you show all workings where necessary.
Define a polynomial and provide an example.
In your answer, include the degree of the polynomial and explain the significance of the degree in determining the polynomial's behaviour.
Factor the polynomial (x^2 - 5x + 6).
Show all steps taken to factor the polynomial completely and state the roots of the equation.
What is the Remainder Theorem?
Demonstrate your understanding by applying it to find the remainder of the polynomial (P(x) = 2x^3 - 3x^2 + 4) when divided by (x - 2).
Explain how to perform polynomial long division.
Use the polynomial (4x^3 + 2x^2 - 6) divided by (2x + 1) as an example. Show the step-by-step process.
Describe the difference between a polynomial function and a polynomial expression.
Include examples to illustrate your points, ensuring to highlight their respective characteristics.
When you respond, please ensure sufficient clarity in your explanations, demonstrating a thorough understanding of each concept related to polynomials. This will not only reflect your grasp of the topic but also demonstrate your mathematical reasoning skills.