Final answer:
The expression (4x⁵-7x²-8x³-4)/(2x³) is simplified by dividing each term in the numerator by 2x³, resulting in the simplified form 2x² - 7/(2x) - 4.
Step-by-step explanation:
To simplify (4x⁵-7x²-8x³-4)/(2x³), we need to perform polynomial division by dividing each term in the numerator by 2x³. This process involves using the Division of Exponentials rule, where we divide the coefficient (number) of each term by 2 and subtract the exponents of the x terms in the numerator by 3 (the exponent in the denominator).
- 4x⁵ divided by 2x³ is 2x²
- 7x² divided by 2x³ becomes -7/(2x)
- 8x³ divided by 2x³ is -4
By following these steps, we get the simplified expression 2x² - 7/(2x) - 4, since the '4' at the end of the original numerator has no 'x' to divide by 2x³ and hence, gets subtracted directly.