Answer :
[tex] \frac{-4x^3+21x^2-23x+6}{x-4} = \frac{(-4 x^{2} +5x-3)(x-4)-6}{x-4} [/tex]
-4x² + 5x - 3
x - 4|-4x³ + 21x² - 23x + 6
-(-4x³ + 16x²)
5x² - 23x
-(-5x² - 20x)
-3x + 6
-(-3x + 12)
-6
x - 4|-4x³ + 21x² - 23x + 6
-(-4x³ + 16x²)
5x² - 23x
-(-5x² - 20x)
-3x + 6
-(-3x + 12)
-6