dividing polynommials

Question

(12x^15n-24x^12n+8x^3n)/(4x^3n)

Answer 1

Try making the following substitutions and then try factoring it out:

12x^15n = (3x^12n)(4x^3n)

24x^12n = (6x^9n)(4x^3n)

8x^3n = (2)(4x^3n)

Answer 2

x^a + x^b = x^(a+b) .....(1) ; x^a / x^b = x^(a-b) ......(2)  ;  x⁰ = 1 .....(3)
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(12x¹⁵ⁿ - 24x¹²ⁿ + 8x³ⁿ) / 4x³ⁿ = 4(3x¹⁵ⁿ - 6x¹²ⁿ + 2x³ⁿ) / 4x³ⁿ , after dividing numerator and denominator by 4 -----> (3x¹⁵ⁿ - 6x¹²ⁿ + 2x³ⁿ) / x³ⁿ , now we have to divide each term in the numerator by denominator by using formulas (2) and (3):
 (3x¹⁵ⁿ / x³ⁿ) - (6x¹²ⁿ / x³ⁿ) + (2x³ⁿ / x³ⁿ) =
  3x^15n-3n       -   6x^12n-3n     +  2x^3n-3n    =
  3x¹²ⁿ           -   6x⁹ⁿ          +  2 .