Question

What is the quotient of \frac{35x^5-20x^4+45x^3}{5x^2}?

Answer 1

To find the quotient of \(\frac{35x^5-20x^4+45x^3}{5x^2}\), we can divide each term in the numerator by \(5x^2\).

1. Divide the first term:
\[
\frac{35x^5}{5x^2} = \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3
\]

2. Divide the second term:
\[
\frac{-20x^4}{5x^2} = \frac{-20}{5} \cdot \frac{x^4}{x^2} = -4x^{4-2} = -4x^2
\]

3. Divide the third term:
\[
\frac{45x^3}{5x^2} = \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x
\]

Now we can combine all these results:

\[
\frac{35x^5-20x^4+45x^3}{5x^2} = 7x^3 - 4x^2 + 9x
\]

Thus, the final quotient is:

\[
\boxed{7x^3 - 4x^2 + 9x}
\]