The decomposition of a polynomial function like \( f(x) = x^3 \) typically involves expressing it in terms of its simpler components, often using linear factors. For \( f(x) = x^3 \), the decomposition can be seen as a factorization process. Here, since \( x^3 \) is already a simple polynomial, its factorization is straightforward.

The function \( f(x) = x^3 \) can be factored as follows:
\[ f(x) = x^3 = x \cdot x \cdot x \]

If we are looking to express this in terms of linear factors:
\[ f(x) = x(x^2) \]
\[ f(x) = x \cdot x \cdot x \]

In this context, \( f(x) = x^3 \) doesn't have any further decomposition in terms of linear factors beyond \( x \cdot x \cdot x \).

However, if we consider the roots of the polynomial, \( f(x) = 0 \) leads to the root \( x = 0 \) with a multiplicity of 3. So, the polynomial can be written in terms of its roots as:
\[ f(x) = (x - 0)^3 = x^3 \]

Would you like details or have any questions? Here are some related questions you might be interested in:

1. How do you decompose a quadratic polynomial?
2. What is the factor theorem and how does it apply to polynomials?
3. How do you find the roots of higher-degree polynomials?
4. What is the role of the fundamental theorem of algebra in polynomial factorization?
5. How can polynomial long division be used in the factorization process?

**Tip:** When decomposing polynomials, always start by looking for common factors and use the factor theorem to identify roots that can help in factorization.

Explore the decomposition of the polynomial function f(x)=x³ into its linear factors and roots. Learn how to factorize polynomials and understand the role of the Fundamental Theorem of Algebra. Suitable for high school students studying algebra and polynomial functions.

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