factor $$ 6 x^{4}+8 x^{2}=26 x^{3} $$

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To factor the polynomial $$ 6x^{4} + 8x^{2} = 26x^{3} $$, follow these steps:

1. **Rewrite in Standard Form:**
   
   First, bring all terms to one side to get the polynomial in standard form:
   $$
   6x^4 - 26x^3 + 8x^2 = 0
   $$

2. **Factor Out the Greatest Common Factor (GCF):**
   
   Identify and factor out the GCF from all terms. The GCF here is $$ 2x^2 $$:
   $$
   2x^2 (3x^2 - 13x + 4) = 0
   $$

3. **Factor the Quadratic Expression:**
   
   Now, factor the quadratic $$ 3x^2 - 13x + 4 $$. Look for two numbers that multiply to $$ 3 \times 4 = 12 $$ and add up to $$-13$$. These numbers are $$-12$$ and $$-1$$.

Rewrite the quadratic using these numbers:
   $$
   3x^2 - 12x - x + 4
   $$
   
   Factor by grouping:
   $$
   3x(x - 4) - 1(x - 4) = (3x - 1)(x - 4)
   $$

4. **Combine All Factors:**
   
   Putting it all together, the fully factored form of the original polynomial is:
   $$
   2x^2 (3x - 1)(x - 4) = 0
   $$

**Final Factored Form:**
$$
2x^2 (3x - 1)(x - 4)
$$
The polynomial factors to $$ 2x^2 (3x - 1)(x - 4) $$.

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