Question

Разложите на множители квадратный трехчлен
x^2-16x+60
x^2+20x-96
x^2-4x-77
x^2-4x-96

Answer 1

$x^{2} -16x +6 = 0 \ D = 16^{2} - 6*4 = 256-240 = 16 \ X1 = frac{16-4}{2} = 6 \ X2= frac{16+4}{2} = 10 \ (x - X1)(x- X2) = 0 \ <strong>(x-6)(x-10) = 0 </strong>$

$x^{2} +20x -96 = 0 \ D= 20^{2} - (-96*4)=400+384= 784 \ X1 = frac{-20+28}{2} = 4 \ X2= frac{-20-28}{2} = -24 \ (x -X1)(x-X2) = 0 \ <strong>(x-4)(x+24) = 0 </strong>$


$x^{2} -4x - 77 = 0 \ D= 4^{2} - (-77*4) = 16+308= 324 \ X1= frac{4+18}{2} = 11 \ X2 = frac{4-18}{2} = -7 \ (x -X1) (x-X2) = 0 \ <strong>(x-11)(x+7) = 0</strong>$

$x^{2} - 4x- 96 = 0 \ D= 4^{2} - (-96*4) = 400 \ X1= frac{4+20}{2} = 12 \ X2= frac{4-20}{2} = -8 \ (x-X1)(x-X2) = 0 \ <strong>(x-12)(x+8) = 0</strong>$

Answer 2

1)...= (x-6)(x-10) 2)...=(x+24)(x-4) 3)...=(x+7)(x-11) 4)...=(x-12)(x+8)