3x^2+5x-7
I want to make sure this is an error in the book.
You can't factor this right?
I certainly hope you mean $\displaystyle \displaystyle 3\left[x - \left(-\frac{5}{6} + \frac{\sqrt{109}}{6}\right)\right]\left[x - \left(-\frac{5}{6} - \frac{\sqrt{109}}{6}\right)\right]$...
$\displaystyle \displaystyle \begin{align*} 3x^2 + 5x - 7 &= 3 \left( x^2 + \frac{5}{3}x - \frac{7}{3} \right) \\ &= 3 \left[ x^2 + \frac{5}{3}x + \left( \frac{5}{6} \right)^2 - \left(\frac{5}{6}\right)^2 - \frac{7}{3}\right] \\ &= 3\left[\left(x + \frac{5}{6}\right)^2 - \frac{25}{36} - \frac{84}{36}\right] \\ &= 3\left[\left(x + \frac{5}{6}\right)^2 - \frac{109}{36}\right] \\ &= 3\left[\left(x + \frac{5}{6}\right)^2 - \left(\frac{\sqrt{109}}{6}\right)^2\right] \\ &= 3\left(x + \frac{5}{6} - \frac{\sqrt{109}}{6}\right)\left(x + \frac{5}{6} + \frac{\sqrt{109}}{6}\right) \end{align*}$