Started: Jul 10 at 7:13pm 10 Quiz Instructions Show Instructions 55 Question 4 Use synthetic division. Leave your answer in fraction form. \[ \left(4 x^{5}+23 x^{4}+14 x^{3}+x^{2}+28 x-12\right) \div(x+5) \] $4 x^{4}+x^{3}-2 x^{2}+4 x-5-\frac{6}{x+5}$ $4 x^{4}+3 x^{3}-x^{2}+6 x-2-\frac{2}{x+5}$ $4 x^{4}+2 x^{3}+x^{2}-3 x-4-\frac{10}{x+5}$ $4 x^{4}-2 x^{3}+4 x-1-\frac{12}{x+5}$

Step 1 ：The given problem is to perform synthetic division on the polynomial \(4x^{5} + 23x^{4} + 14x^{3} + x^{2} + 28x - 12\) by the divisor \(x + 5\).

Step 2 ：Synthetic division is a shorthand method of dividing polynomials where we divide the coefficients of the polynomial with the divisor.

Step 3 ：Performing the synthetic division, we get the quotient as \(4x^{4} + 3x^{3} - x^{2} + 6x - 2\) and the remainder as \(-\frac{2}{x+5}\).

Step 4 ：\(\boxed{4x^{4} + 3x^{3} - x^{2} + 6x - 2 - \frac{2}{x+5}}\) is the final result of the synthetic division.