Answer
$3x^4 - \frac{2}{x}$
Work Step by Step
Given: $(12x^8 - 8x^3) \div 4x^4$
$(12x^8 - 8x^3) \div 4x^4 = \frac{12x^8}{4x^4} - \frac{8x^3}{4x^4}$
(distributive law)
Next, separate the coefficient from the x terms.
$\frac{12x^8}{4x^4} - \frac{8x^3}{4x^4} = (\frac{12}{4})(\frac{x^8}{x^4}) - (\frac{8}{4})(\frac{x^3}{x^4})$
$= (3)(x^{8-4}) - (2)(x^{3-4})$
(Use the second law of indices with the same base: $a^{m} \div a^{y} = a^{m-n}$
$= (3)(x^4) - (2)(x^{-1})$
Convert all terms to a positive index.
$= 3x^4 - \frac{2}{x}$
