(4) \( \left(-3 x^{3}+7 x^{2}+27 x-28\right) \div(x-4) \)

To evaluate \( \left(-3 x^{3}+7 x^{2}+27 x-28\right) \div(x-4) \), we can use synthetic division or polynomial long division. If you set up synthetic division with \(4\) (the root of \(x-4=0\)), you will get the coefficients \(-3, 7, 27, -28\). Performing the division, you will find the result is \(-3x^2 + 31x + 124\) with a remainder of \(0\). So, \( \left(-3 x^{3}+7 x^{2}+27 x-28\right) \div(x-4) = -3x^2 + 31x + 124\). Here's a great tip: Always check your work by substituting \(x=4\) back into both the original polynomial and the quotient to see if they yield the same value! Also, make sure to double-check for any common factors or errors before concluding your division, as overlooking a small mistake can lead you astray in polynomial division!