factor \( 6 x^{4}+8 x^{2}=26 x^{3} \)

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:** \[ 2x^2 (3x - 1)(x - 4) \]