$x^2 - 3x - 18 = 0$
$D = b^2 - 4ac = (-3)^2 - 4 * 1 * (-18) = 9 + 72 = 81 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{81}}{2 * 1} = \frac{3 + 9}{2} = \frac{12}{2} = 6$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{3 - \sqrt{81}}{2 * 1} = \frac{3 - 9}{2} = \frac{-6}{2} = -3$
$x^2 - 3x - 18 = (x - 6)(x - (-3)) = (x - 6)(x + 3)$
Ответ:$x^2 - 3x - 18 = (x - 6)(x + 3)$

$x^2 + 5x - 14 = 0$
$D = b^2 - 4ac = 5^2 - 4 * 1 * (-14) = 25 + 56 = 81 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-5 + \sqrt{81}}{2 * 1} = \frac{-5 + 9}{2} = \frac{4}{2} = 2$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-5 - \sqrt{81}}{2 * 1} = \frac{-5 - 9}{2} = \frac{-14}{2} = -7$
$x^2 + 5x - 14 = (x - 2)(x - (-7)) = (x - 2)(x + 7)$
Ответ: $x^2 + 5x - 14 = (x - 2)(x + 7)$

$-x^2 + 3x + 4 = 0$
$D = b^2 - 4ac = 3^2 - 4 * (-1) * 4 = 9 + 16 = 25 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-3 + \sqrt{25}}{2 * (-1)} = \frac{-3 + 5}{-2} = \frac{2}{-2} = -1$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-3 - \sqrt{25}}{2 * (-1)} = \frac{-3 - 5}{-2} = \frac{-8}{-2} = 4$
$-x^2 + 3x + 4 = -(x - (-1))(x - 4) = (x + 1)(4 - x)$
Ответ: $-x^2 + 3x + 4 = (x + 1)(4 - x)$

$5x^2 + 8x - 4 = 0$
$D = b^2 - 4ac = 8^2 - 4 * 5 * (-4) = 64 + 80 = 144 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-8 + \sqrt{144}}{2 * 5} = \frac{-8 + 12}{10} = \frac{4}{10} = 0,4$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-8 - \sqrt{144}}{2 * 5} = \frac{-8 - 12}{10} = \frac{-20}{10} = -2$
$5x^2 + 8x - 4 = 5(x - 0,4)(x - (-2)) = (5x - 2)(x + 2)$
Ответ: $5x^2 + 8x - 4 = (5x - 2)(x + 2)$

$2a^2 - 3a + 1 = 0$
$D = b^2 - 4ac = (-3)^2 - 4 * 2 * 1 = 9 + 8 = 1 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{1}}{2 * 2} = \frac{3 + 1}{4} = \frac{4}{4} = 1$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{3 - \sqrt{1}}{2 * 2} = \frac{3 - 1}{4} = \frac{2}{4} = 0,5$
$2a^2 - 3a + 1 = 2(a - 1)(a - 0,5) = (a - 1)(2a - 1)$
Ответ: $2a^2 - 3a + 1 = (a - 1)(2a - 1)$

$4b^2 - 11b - 3 = 0$
$D = b^2 - 4ac = (-11)^2 - 4 * 4 * (-3) = 121 + 48 = 169 > 0$
$b_1 = \frac{-b + \sqrt{D}}{2a} = \frac{11 + \sqrt{169}}{2 * 4} = \frac{11 + 13}{8} = \frac{24}{8} = 3$
$b_2 = \frac{-b - \sqrt{D}}{2a} = \frac{11 - \sqrt{169}}{2 * 4} = \frac{11 - 13}{8} = \frac{-2}{8} = -\frac{1}{4}$
$4b^2 - 11b - 3 = 4(b - 3)(b - (-\frac{1}{4})) = 4(b - 3)(b + \frac{1}{4}) = (b - 3)(4b + 1)$
Ответ: $4b^2 - 11b - 3 = (b - 3)(4b + 1)$

$-\frac{1}{4}x^2 - 2x - 3 = 0$
$D = b^2 - 4ac = (-2)^2 - 4 * (-\frac{1}{4}) * (-3) = 4 - 3 = 1 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{2 + \sqrt{1}}{2 * (-\frac{1}{4})} = \frac{2 + 1}{-\frac{1}{2}} = \frac{3}{-\frac{1}{2}} = -6$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{2 - \sqrt{1}}{2 * (-\frac{1}{4})} = \frac{2 - 1}{-\frac{1}{2}} = \frac{1}{-\frac{1}{2}} = -2$
$-\frac{1}{4}x^2 - 2x - 3 = -\frac{1}{4}(x - (-6))(x - (-2)) = -\frac{1}{4}(x + 6)(x + 2)$
Ответ: $-\frac{1}{4}x^2 - 2x - 3 = -\frac{1}{4}(x + 6)(x + 2)$

$0,3m^2 - 3m + 7,5 = 0$
$D = b^2 - 4ac = (-3)^2 - 4 * 0,3 * 7,5 = 9 - 9 = 0$
$m = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{0}}{2 * 0,3} = \frac{3}{0,6} = \frac{30}{6} = 5$
$0,3m^2 - 3m + 7,5 = 0,3(m - 5)(m - 5) = 0,3(m - 5)^2$
Ответ: $0,3m^2 - 3m + 7,5 = 0,3(m - 5)^2$

$x^2 - 2x - 2 = 0$
$D = b^2 - 4ac = (-2)^2 - 4 * 1 * (-2) = 4 + 8 = 12 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{2 + \sqrt{12}}{2 * 1} = \frac{2 + \sqrt{4 * 3}}{2} = \frac{2 + 2\sqrt{3}}{2} = \frac{2(1 + \sqrt{3})}{2} = 1 + \sqrt{3}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{2 - \sqrt{12}}{2 * 1} = \frac{2 - \sqrt{4 * 3}}{2} = \frac{2 - 2\sqrt{3}}{2} = \frac{2(1 - \sqrt{3})}{2} = 1 - \sqrt{3}$
$x^2 - 2x - 2 = (x - (1 + \sqrt{3}))(x - (1 - \sqrt{3})) = (x - 1 - \sqrt{3})(x - 1 + \sqrt{3})$
Ответ:$x^2 - 2x - 2 = (x - 1 - \sqrt{3})(x - 1 + \sqrt{3})$