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We are tasked with finding the roots of the function \( f(x) = x^3 + 3x^2 - x - 3 \), given that \( f(1) = 0 \), using the Remainder Theorem.

### Remainder Theorem:
The Remainder Theorem tells us that if \( f(c) = 0 \), then \( x - c \) is a factor of the polynomial \( f(x) \). Since \( f(1) = 0 \), \( x - 1 \) is a factor of \( f(x) \).

### Steps:
1. **Synthetic Division**: We'll use synthetic division to divide \( f(x) \) by \( (x - 1) \).

   The coefficients of \( f(x) = x^3 + 3x^2 - x - 3 \) are \( 1, 3, -1, -3 \). We perform synthetic division with \( 1 \) as the divisor:

   \[
   \begin{array}{r|rrrr}
   1 & 1 & 3 & -1 & -3 \\
     &   & 1 & 4  &

If f(1) = 0, what are all the roots of the function f(x) = x^3 + 3x^2 - x - 3? Use the Remainder Theorem.

Learn how to find all the roots of the cubic polynomial f(x) = x^3 + 3x^2 - x - 3 using the Remainder Theorem. This problem covers key algebraic concepts and is suitable for students in Grades 10-12.

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