Factoring and Solving the Expression (x+1)(x1)(x3)
The expression (x+1)(x1)(x3) is a factored polynomial. Let's explore its properties and how to solve it.
Understanding the Factored Form
The expression is already in factored form, meaning it's expressed as a product of simpler expressions. This form is helpful for:

Finding the roots (or zeros): The roots are the values of x that make the expression equal to zero. Since the expression is a product, it equals zero when any of the factors equals zero. Therefore, the roots are:
 x + 1 = 0 => x = 1
 x  1 = 0 => x = 1
 x  3 = 0 => x = 3

Graphing the function: The roots represent the points where the graph of the function y = (x+1)(x1)(x3) crosses the xaxis. The factored form also tells us the behavior of the function near the roots.
Expanding the Expression
We can expand the expression to get a polynomial in standard form:

Start with the first two factors: (x+1)(x1) = x²  1 (This is a difference of squares pattern)

Multiply the result by the third factor: (x²  1)(x3) = x³  3x²  x + 3
Therefore, the expanded form of the expression is x³  3x²  x + 3.
Applications
This expression can be used in various mathematical contexts, such as:
 Solving equations: Setting the expression equal to zero and solving for x would give us the same roots we found earlier.
 Finding the zeros of a polynomial function: The roots of the expression represent the xintercepts of the function y = (x+1)(x1)(x3).
 Analyzing the behavior of the function: The factored form provides insights into the function's behavior around its roots.
Conclusion
The expression (x+1)(x1)(x3) is a factored polynomial with roots at x = 1, x = 1, and x = 3. Understanding the factored form allows us to easily find the roots and analyze the behavior of the corresponding function. It's important to remember that this expression can be expanded into a standard polynomial form, which can be useful in different applications.