Разложите на множители квадратный трёхчлен 3 х^2+7x-6 x^2-10x+21 5x^2+9x-2

1) f (x) = 3 х^2 + 7x - 6;

D = 7^2 + 4 * 3 * 6 = 49 + 72 = 121 = 11^2; x = (-7 ± 11) / 6; x1 = (-7 - 11) / 6 = - 18/6 = - 3; x2 = (-7 + 11) / 6 = 4/6 = 2/3; 3 х^2 + 7x - 6 = 3 (x + 3) (x - 2/3) = (x + 3) (3x - 2).

2) g (x) = x^2 - 10x + 21;

D/4 = 5^2 - 21 = 25 - 21 = 4 = 2^2; x = 5 ± 2; x1 = 5 - 2 = 3; x2 = 5 + 2 = 7; x^2 - 10x + 21 = (x - 3) (x - 7).

3) h (x) = 5x^2 + 9x - 2;

D = 9^2 + 4 * 5 * 2 = 81 + 40 = 121 = 11^2; x = (-9 ± 11) / 5; x1 = (-9 - 11) / 10 = - 20/10 = - 2; x2 = (-9 + 11) / 10 = 1/5; 5x^2 + 9x - 2 = 5 (x + 2) (x - 1/5) = (x + 2) (5x - 1).

Ответ:

1) (x + 3) (3x - 2); 2) (x - 3) (x - 7); 3) (x + 2) (5x - 1).