\( 1 \ll \begin{array}{l}\begin{array}{r}5 x^{4}+6 x^{2}-2 x \\ -\left(-7 x^{4}-2 x^{2}+3 x\right)\end{array} \\ \begin{array}{l}\text { The difference is } \square . \\ \text { (Simplify your answer.) }\end{array}\end{array} \)

To find the difference, we start by simplifying the expression inside the parentheses: \[ 5x^{4} + 6x^{2} - 2x - \left(-7x^{4} - 2x^{2} + 3x\right) \] First, we'll distribute the negative sign: \[ 5x^{4} + 6x^{2} - 2x + 7x^{4} + 2x^{2} - 3x \] Next, we'll combine like terms: - For \(x^4\): \(5x^{4} + 7x^{4} = 12x^{4}\) - For \(x^{2}\): \(6x^{2} + 2x^{2} = 8x^{2}\) - For \(x\): \(-2x - 3x = -5x\) Putting it all together, we get: \[ 12x^{4} + 8x^{2} - 5x \] So the simplified answer for the difference is: \[ \boxed{12x^{4} + 8x^{2} - 5x} \]