Let's simplify the given expression:

$\frac{x^4 - 16}{x - 4}$

Step 1: Factor the numerator

The numerator is a difference of squares:

$x^4 - 16 = (x^2 - 4)(x^2 + 4)$

Since $x^2 - 4$ is also a difference of squares, we further factor it:

$x^2 - 4 = (x - 2)(x + 2)$

Thus, the numerator fully factors as:

$(x - 2)(x + 2)(x^2 + 4)$

Step 2: Cancel common factors

Since the denominator is $x - 4$, no direct common factors exist in the numerator. So, the expression cannot be simplified further.

Thus, the simplified form remains:

$\frac{(x - 2)(x + 2)(x^2 + 4)}{x - 4}$

This is the factored form of the given expression.

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Related Questions:

1. How do you factor higher-degree polynomials like $x^4 - 16$?
2. What is the difference of squares, and how is it applied in factoring?
3. Can you explain how to simplify rational expressions with polynomials?
4. What happens if $x = 4$ in the given expression?
5. How do you handle cases where the denominator is a factor of the numerator?

Tip: Always check if a polynomial can be factored using special formulas like the difference of squares!