Разложите на множители квадратный трехчлен: 30y^2-10y-100.

\[30y² - 10y - 100 = 0\ \ \ |\ :10\]

\[3y^{2} - y - 10 = 0\]

\[D = 1 + 120 = 121\]

\[y_{1} = \frac{1 + 11}{6} = 2;\ \ \ \]

\[y_{2} = \frac{1 - 11}{6} = - \frac{10}{6} = - \frac{5}{3}.\]

\[30y^{2} - 10y - 100 =\]

\[= 30 \cdot (y - 2)\left( y + \frac{5}{3} \right) =\]

\[= 10 \cdot (y - 2)(3y + 5).\]