Final answer:
To divide the polynomial 36y^4 + 30y^3 by 6y, you separately divide each term to get 6y^3 + 5y^2.
Step-by-step explanation:
The student is asking how to divide a polynomial by a monomial. Specifically, they want to divide 36y^4 + 30y^3 by 6y. To accomplish this, we need to divide each term in the numerator separately by the term in the denominator and then combine the results.To divide the expression 36y^4 + 30y^3 by 6y, you can rewrite it as (36y^4 + 30y^3) / (6y). To divide the terms, you can divide the coefficients and subtract the exponents of the variables. So, (36/6)y^(4-1) + (30/6)y^(3-1) = 6y^3 + 5y^2. Therefore, the result of dividing 36y^4 + 30y^3 by 6y is 6y^3 + 5y^2.
- Divide 36y^4 by 6y: This gives us 6y^3.
- Divide 30y^3 by 6y: This gives us 5y^2.
Combining these results gives us the final answer: 6y^3 + 5y^2.