Question

Simplify \frac{15x^5-3x^3+9x^2}{3x}. Write your answer in standard form

Answer 1

To simplify the expression \(\frac{15x^5 - 3x^3 + 9x^2}{3x}\), we can divide each term in the numerator by the denominator \(3x\).

Step 1: Divide each term in the numerator by \(3x\).

\[
\frac{15x^5}{3x} - \frac{3x^3}{3x} + \frac{9x^2}{3x}
\]

Step 2: Simplify each term individually.

- For the first term:
\[
\frac{15x^5}{3x} = \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4
\]

- For the second term:
\[
\frac{3x^3}{3x} = \frac{3}{3} \cdot \frac{x^3}{x} = 1 \cdot x^{3-1} = x^2
\]

- For the third term:
\[
\frac{9x^2}{3x} = \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x
\]

Step 3: Combine the simplified terms.

\[
5x^4 - x^2 + 3x
\]

Step 4: Write the final answer in standard form.

The final simplified expression is:
\[
\boxed{5x^4 + 3x - x^2}
\]

To write it in standard form (arranging terms in descending powers of \(x\)), we rearrange it to:
\[
\boxed{5x^4 - x^2 + 3x}
\]