Answer:4x^2 - kx + 4 divided by x + 7, we need to perform polynomial division. Since the user has provided an expression to be divided, it implies we are likely looking for the quotient and remainder, or perhaps a condition on 'k' if the division is meant to be exact.Let's use polynomial long division or synthetic division. Synthetic division is generally faster for divisors of the form (x - a). In this case, our divisor is (x + 7), which means a = -7.We are dividing 4x^2 - kx + 4 by x + 7.Using synthetic division with a = -7:-7 | 4 -k 4 | -28 7k + 196 ------------------- 4 -k-28 7k + 200The last number in the bottom row is the remainder, and the other numbers are the coefficients of the quotient.So, the quotient is 4x + (-k - 28), and the remainder is 7k + 200.Therefore, when 4x^2 - kx + 4 is divided by x + 7, the result is:4x - (k + 28) + \\frac{7k + 200}{x + 7}