Question

Divide. (4x^4 - 4x^2 - x-3) = (2x^2 – 3)​

Answer 1

• 
  `(4x^4 - 4x^2 - x - 3)/(2x^2 - 3)`

Explanation:

Step 1:

• Simplify:
  `(4x^4 - 4x^2 - x - 3)/(2x^2 - 3)`

Checking for a perfect cube:

• 4x⁴ - 4x² - x - 3 is not a perfect cube.

Trying to factor by pulling out:

• Factoring: 4x⁴ - 4x² - x - 3
• Thoughtfully split the expression at hand into groups, each group having two terms:
• Group 1: - x - 3
• Group 2: 4x⁴ - 4x³
• Pull out from each group separately:
• Group 1: (x + 3) • (-1)
• Group 2: (x² - 1) • (4x²)
• Bad news!! Factoring by pulling out fails:
• The groups have no common factor and can not be added up to form a multiplication

Final result:

• 
  `(4x^4 - 4x^2 - x - 3)/(2x^2 - 3)`