Question

Find the quotient of minus, 40, z, squared, plus, 40, z−40z
2
+40z divided by 5, z5z.

Answer 1

To find the quotient of \(-40z^2 + 40z\) divided by \(5z\), we can follow these steps:

1. **Rewrite the expression**: We need to divide \(-40z^2 + 40z\) by \(5z\).

2. **Factor the numerator**: Notice that we can factor out \(40z\) from the numerator:
\[
-40z^2 + 40z = 40z(-z + 1)
\]

3. **Set up the division**: Now our expression looks like:
\[
\frac{40z(-z + 1)}{5z}
\]

4. **Cancel out \(z\)**: Since \(z\) is in both the numerator and the denominator (assuming \(z \neq 0\)):
\[
\frac{40(-z + 1)}{5}
\]

5. **Simplify the fraction**: Now simplify \( \frac{40}{5} \) to get:
\[
8(-z + 1)
\]

6. **Distribute**: Finally, distribute the \(8\):
\[
-8z + 8
\]

So, the quotient of \(-40z^2 + 40z\) divided by \(5z\) is:
\[
-8z + 8
\]