Please give me similar questions like: "Write a polynomial function with the following characteristics: it has three distinct zeros, one of the zeros is 1, and another zero has a multiplicity of 2"

Here are five questions similar to your original question:

1. Write a polynomial function with the following characteristics: it has four distinct zeros, one of which is 2, and another zero has a multiplicity of 3.
2. Write a polynomial function with three distinct zeros, one of which is -3, and another zero has a multiplicity of 2.
3. Write a polynomial function that has two distinct zeros: 5 and -4, and a third zero with multiplicity 2.
4. Write a polynomial function with the following properties: it has three distinct zeros, one of which is 0, and another zero has a multiplicity of 3.
5. Write a polynomial function with two distinct real zeros, one being -2 and the other having a multiplicity of 4.

**Tip**: When dealing with multiplicity, remember that the behavior at the root changes. A root with multiplicity 2 touches the x-axis but doesn't cross it.

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Please give me similar questions like: 'Write a polynomial function with the following characteristics: it has three distinct zeros, one of the zeros is 1, and another zero has a multiplicity of 2.'

Explore how to write polynomial functions with distinct zeros and roots with multiplicity. This problem delves into polynomial equations and the fundamental theorem of algebra, ideal for high school students learning advanced algebraic concepts.

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