For all nonzero values of x, (12x^6 - 9x^2)/3x^2

For all nonzero values of x, (12x6 - 9x2)/3x2 = ?

  1. 4x3 - 3x
  2. 4x3 - 3
  3. 4x4 - 9x2
  4. 4x4 - 3x
  5. 4x4 - 3

Answer

The correct answer is E.

Factor the greatest common factor out of the numerator and then cancel factors of the numerator with identical factors of the denominator.

(12x6 - 9x2)/3x2

= 3x2(4x4 - 3)/3x2

= 4x4 - 3

Alternate Solution

(12x6 - 9x2)/3x2

= 12x6/3x2 - 9x2/3x2

= 4x4 - 3