Ответы
Ответ дал:
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Первый способ:
![{x}^{2} + 4x - 32 = {x}^{2} + 4x + 4 - 36 = {(x + 2)}^{2} - 36 = {(x + 2)}^{2} - {6}^{2} = (x + 2 + 6)(x + 2 - 6) = (x + 8)(x - 4) {x}^{2} + 4x - 32 = {x}^{2} + 4x + 4 - 36 = {(x + 2)}^{2} - 36 = {(x + 2)}^{2} - {6}^{2} = (x + 2 + 6)(x + 2 - 6) = (x + 8)(x - 4)](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++%2B+4x+-+32+%3D++%7Bx%7D%5E%7B2%7D++%2B+4x+%2B+4+-+36+%3D++%7B%28x+%2B+2%29%7D%5E%7B2%7D++-+36+%3D++%7B%28x+%2B+2%29%7D%5E%7B2%7D++-++%7B6%7D%5E%7B2%7D++%3D+%28x+%2B+2+%2B+6%29%28x+%2B+2+-+6%29+%3D+%28x+%2B+8%29%28x+-+4%29)
Второй способ:
ax^2 + bx + c = a*(x - x1)(x - x2)
найдем корни уравнения x^2 + 4x - 32 = 0:
D = b^2 - 4ac = 16 - 4*(-32) = 144
x1 = (-4 + 12)/2 = 8/2 = 4
x2 = (-4 - 12)/2 = -16/2 = -8
![{x}^{2} + 4x - 32 = (x - 4)(x + 8) {x}^{2} + 4x - 32 = (x - 4)(x + 8)](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++%2B+4x+-+32+%3D+%28x+-+4%29%28x+%2B+8%29)
Второй способ:
ax^2 + bx + c = a*(x - x1)(x - x2)
найдем корни уравнения x^2 + 4x - 32 = 0:
D = b^2 - 4ac = 16 - 4*(-32) = 144
x1 = (-4 + 12)/2 = 8/2 = 4
x2 = (-4 - 12)/2 = -16/2 = -8
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