Divide. Assume that no denominator equals zero. \( \left(-5 x^{6}+4 x^{7}+5 x^{6}\right) \div x^{3} \) \( \begin{array}{ll}\text { a. }-5 x^{9}+4 x^{10}+5 x^{9} & \text { c. }-5 x^{-3}+4 x^{-4}+5 x^{-3} \\ \text { b. }-5 x^{18}+4 x^{7}+5 x^{6} & \text { d. }-5 x^{3}+4 x^{4}+5 x^{3}\end{array} \)

To simplify the expression \( \left(-5 x^{6}+4 x^{7}+5 x^{6}\right) \div x^{3} \), we first combine like terms in the numerator: - \( -5x^6 + 5x^6 = 0 \), so we're left with \( 4x^7 \). Now, we divide \( 4x^7 \) by \( x^3 \): \[ \frac{4x^7}{x^3} = 4x^{7-3} = 4x^4. \] Thus, the simplified form is \( 4x^4 \). Looking at the options provided, we can observe none match \( 4x^4 \) directly. Therefore, it's not included in the answers, but the most probable option could relate to a misunderstanding or miscalculation. When presented with polynomial divisions, always remember to first combine like terms properly, and then apply the power rule for division. In this case, dividing by \( x^n \) simply means subtracting \( n \) from the exponent of \( x \). Keep an eye out for those pesky negative signs and terms that can be zeroed out!