Question

Divide the polynomials.
Simplify your answer as much (-10y⁴+15y³-2y²+6y-2)-:(5y³)

Answer 1

To divide the polynomial (-10y⁴+15y³-2y²+6y-2) by (5y³), use polynomial division. The simplified answer is -2y + 3 - (2y²-6y+2) / 5y³.

Step-by-step explanation:

To divide the polynomials (-10y⁴+15y³-2y²+6y-2) by (5y³), we use the rules of polynomial division:

1. Divide the first term of the numerator by the first term of the denominator, which gives us -10y⁴ / 5y³ = -2y.
2. Now multiply this result by the denominator (5y³), giving us -2y * 5y³ = -10y⁴.
3. Subtract this result from the numerator, (-10y⁴+15y³-2y²+6y-2) - (-10y⁴) = 15y³-2y²+6y-2.
4. Repeat the process with this new polynomial (15y³-2y²+6y-2).
5. Finally, we obtain our simplified answer: -2y + 3 - (2y²-6y+2) / 5y³.