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Find a polynomial of degree n that has only the given zero(s). (There are many correct answers).

A) x^5
B) x^5 + 2x^3
C) x^5 - 4x^2
D) x^5 + 3x^4 - 2x^3 - 5x^2 + x

User Edthrn
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1 Answer

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Final answer:

The student seeks polynomials of degree n that only have x=0 as their zero. Any polynomial where x=0 makes it zero, like x^n, is a valid answer. The provided options are all correct examples of such polynomials.

Step-by-step explanation:

The student is asking to find a polynomial of degree n that has only the given zero(s). To find such a polynomial, we need to consider that if a polynomial has a zero at x, it means that x is a root of the polynomial. If we take the simplest case, a polynomial of degree n with a zero at x = 0, is x^n. Therefore, polynomials given in options A, B, C, and D all have a zero at x = 0 and are of different degrees (the highest power of x indicates the degree of the polynomial).

For example, consider option A x^5, which is a polynomial of degree 5 and has a zero at x = 0. Similarly, other options are also polynomials with various degrees having a zero at x = 0. However, without additional zeros provided or a specific degree n mentioned, any polynomial that can be constructed such that it equals zero when x = 0 would be an acceptable answer.

User SkeetJon
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