To solve the cubic equation \( 6x^3 + x^2 - 216x - 36 = 0 \), we'll start by looking for possible rational roots using the Rational Root Theorem and then use polynomial division if we find a root.

### Step 1: Identify Possible Rational Roots
The Rational Root Theorem suggests that possible rational roots are the factors of the constant term (-36) divided by the factors of the leading coefficient (6).

- Factors of \(-36\): \(\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 9, \pm 12, \pm 18, \pm 36\

Explore the step-by-step process to solve the cubic equation 6x^3 + x^2 - 216x - 36 using the Rational Root Theorem and Polynomial Division. This problem is designed for high school students in Grades 10-12, covering key algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation