Question

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

Answer 1

Answer:

• $\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$

Step-by-step explanation:

Step 1:

• Simplify: $\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$

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:

• $\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$