To complete the square for the polynomial \( f^2 - 3f \), we need to find a number that makes it a perfect-square quadratic.
- Start with the coefficient of \( f \), which is \(-3\).
- Divide this coefficient by 2: \[ -\frac{3}{2} \]
- Square the result: \[ \left(-\frac{3}{2}\right)^2 = \frac{9}{4} \]
Now, we add \(\frac{9}{4}\) to the expression to complete the square. Therefore, the completed square version of the polynomial is:
\[ f^2 - 3f + \frac{9}{4} \]
With this, the polynomial \( f^2 - 3f + \frac{9}{4} \) can be factored as: \[ \left(f - \frac{3}{2}\right)^2 \]
So, the number that makes the polynomial a perfect-square quadratic is:
\[ \frac{9}{4} \]
1 answer