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)