Question

Розкладіть квадратний тричлен на множники: 1) x² + 3x - 4; 2) - 2x² + 7x - 3

Answer 1

$1) {x}^{2} + 3x - 4 = 0 \\ d = 9 - 4 \times 1 \times ( - 4) = 9 + 16 = 25 = {5}^{2} \\ x1 = \frac{ - 3 + 5}{2} = \frac{2}{2} = 1 \\ x2 = \frac{ - 3 - 5}{2} = \frac{ - 8}{2} = - 4 \\ - 2 {x}^{2} + 7x - 3 = 0 \\ 2 {x}^{2} - 7x + 3 = 0 \\ d = 49 - 4 \times 2 \times 3 = 49 - 24 = 25 = {5}^{2} \\ x1 = \frac{7 + 5}{4} = \frac{12}{4} = 3 \\ x2 = \frac{7 - 5}{4} = \frac{2}{4} = \frac{1}{2} = 0.5$

Answer 2

Ответ:

1.  х²-3х-4=х²+4х--4=х(х+4)-(х+4)=(х+4)(х-1)

2.  -2х²+7х-3=-2х²+6х+х-3=2х(х-3)+х-3=(х-3)(-2х+1)