Question
Simplify 15x^5−3x^3+9x^2 divided by 3x . Write your answer in standard form.
Answers
GPT-4o mini
To simplify the expression \((15x^5 - 3x^3 + 9x^2) \div (3x)\), we can divide each term in the numerator by \(3x\):
1. Start with the first term \(15x^5\):
\[
\frac{15x^5}{3x} = \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4
\]
2. Next, for the second term \(-3x^3\):
\[
\frac{-3x^3}{3x} = \frac{-3}{3} \cdot \frac{x^3}{x} = -1 \cdot x^{3-1} = -x^2
\]
3. Finally, for the third term \(9x^2\):
\[
\frac{9x^2}{3x} = \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x
\]
Now, combining these results gives us:
\[
5x^4 - x^2 + 3x
\]
Next, we write this in standard form, which is typically ordered by the degree of the terms (from highest to lowest). Thus, the final simplified expression is:
\[
5x^4 + 3x - x^2
\]
Reordering gives:
\[
5x^4 - x^2 + 3x
\]
So the answer in standard form is:
\[
5x^4 - x^2 + 3x
\]
1. Start with the first term \(15x^5\):
\[
\frac{15x^5}{3x} = \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4
\]
2. Next, for the second term \(-3x^3\):
\[
\frac{-3x^3}{3x} = \frac{-3}{3} \cdot \frac{x^3}{x} = -1 \cdot x^{3-1} = -x^2
\]
3. Finally, for the third term \(9x^2\):
\[
\frac{9x^2}{3x} = \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x
\]
Now, combining these results gives us:
\[
5x^4 - x^2 + 3x
\]
Next, we write this in standard form, which is typically ordered by the degree of the terms (from highest to lowest). Thus, the final simplified expression is:
\[
5x^4 + 3x - x^2
\]
Reordering gives:
\[
5x^4 - x^2 + 3x
\]
So the answer in standard form is:
\[
5x^4 - x^2 + 3x
\]