To find the quotient of the expression \( \frac{21x^3 + 14x^2 - x}{7x^2} \), we can divide each term in the numerator by the denominator \( 7x^2 \).
-
Divide the first term: \[ \frac{21x^3}{7x^2} = 3x \]
-
Divide the second term: \[ \frac{14x^2}{7x^2} = 2 \]
-
Divide the third term: \[ \frac{-x}{7x^2} = -\frac{1}{7} \cdot \frac{1}{x} = -\frac{1}{7x} \]
Now, combine all the results: \[ 3x + 2 - \frac{1}{7x} \]
Thus, the quotient of the expression \( 21x^3 + 14x^2 - x \) divided by \( 7x^2 \) is: \[ \boxed{3x + 2 - \frac{1}{7x}} \]
This is the answer in standard form.