Final answer:
The expression 6x⁴−15x³−2x²²−10x−4/3x² simplifies to 2x² − 5x-4/3 by factoring out 3x² from each term in the numerator.
Step-by-step explanation:
To evaluate the expression 6x ⁴−15x ³−2x ²²−10x−4/3x², we look for common factors and simplify. Since this expression is in polynomial form and we're dividing by 3x², we can factor out 3x² from each term in the numerator:
6x⁴/3x² = 2x²
15x³/3x² = 5x
2x⁴/3x² = (2x²) ²/3x² = 4x²/3x² = ⅔
10x/3x² = 10/3x
4/3x² = ⅔
Putting it all together, we obtain our simplified expression:
2x² − 5x − ⅔
This corresponds to option B) 2x² − 5x-4/3.