Algebra: A Combined Approach (4th Edition)

The answer is $4x^2 + 16x + 55 + \frac{222}{x - 4}$.
Now, the dividend $4x^3 - 9x + 2$ can be rewritten as $4x^3 + 0x^2 - 9x + 2$. $\space \space \space \space \space \space \space \space \space \space \space \space 4x^2 + 16x + 55$ $x - 4 /\overline{4x^3 + 0x^2 - 9x + 2}$ $\space \space \space \space \space \space \space \space \space \space \space \space \underline{4x^3 - 16x^2}$ $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space 16x^2 - 9x$ $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \underline{16x^2 -64x}$ $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space 55x + 2$ $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \underline{55x - 220}$ $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space 222$ The answer is $4x^2 + 16x + 55 + \frac{222}{x - 4}$.