To solve the equation \( y^4 - 13y + 36 = 0 \), let's attempt to find solutions for \( y \).

### Step-by-step approach:

1. **Look for Rational Solutions:**
   Use the Rational Root Theorem, which suggests that potential rational roots can be factors of the constant term (36) divided by factors of the leading coefficient (1).

   Possible rational roots are \( \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 9, \pm 12, \pm 18, \pm 36 \).

2. **Test for rational roots:**
   We can substitute these values into the equation to see if they yield a solution.

   - Trying \( y = 2 \):

   \[
   2^4 - 13(2) + 36 = 16 - 26 + 36 = 26 \quad \text{(Not zero, so not a solution)}
   \]

   - Trying \( y = -2 \):

   \[
   (-2)^4 - 13(-2) + 36 = 16 + 26 + 36 = 78 \quad \text{(Not zero, so not a solution)}
   \]

   - Trying \( y = 3 \):

   \[
   3^4 - 13(3) + 36 = 81 - 39 + 36 = 78 \quad \text{(Not zero, so not a solution

Learn how to solve the polynomial equation y^4 - 13y + 36 using the Rational Root Theorem. This solution provides a step-by-step process, testing potential rational roots for this fourth-degree equation. Suitable for high school students in Grades 10-12.

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