Question

Divide. Divide \(16 y^{3}-36 y^{2}-64\) by \(-4 y^{2}\).

Short answer

The result of the given division is \(-4 y + 9 + 16/y^{2}\)

Step-by-step solution

Isolate Each Term

Divide the polynomial \(16 y^{3}-36 y^{2}-64\) to isolate each term. Then we have three terms: \(16 y^{3}\), \(-36 y^{2}\), and \(-64\).

Dividing First Term

Divide the first term \(16 y^{3}\) by \(-4 y^{2}\). The y values are subtracted from each other (using the rules of exponents). This results in \(-4 y\).

Dividing Second Term

Next, divide the second term \(-36 y^{2}\) by \(-4 y^{2}\). Because the y values match, they cancel each other out, resulting in 9.

Dividing Third Term

Finally, divide the third term \(-64\) by \(-4 y^{2}\), which gives us \(16/y^{2}\).

Combine All Terms

Combine all the terms obtained from the division to give the final answer. The resulting expression is: \(-4 y + 9 + 16/y^{2}\)