Разложите на множители: 1) x^2 - y^2+14y-49

2) x^2+x-6

3) x^2-4x+3

4) x^3+3x^2-x-3=0

1) x^2 - y^2+14y-49

x ² - (y²-14y+49) = x² - (y-7) ² = (x-y+7) (x+y-7)

2) x^2+x-6 = (x ²+3x) - (2x+6) = x (x+3) - 2 (x+3) = (x+3) (x-2)

3) x^2-4x+3 = (x ²-x) - (3x-3) = x (x-1) - 3 (x-1) = (x-1) (x-3)

4) x^3+3x^2-x-3=0

(x ³-x³) + (4x²-4x) + (3x-3) = 0

x² (x-1) + 4x (x-1) + 3 (x-1) = 0

(x-1) (x²+4x+3) = 0

(x-1) ((x²+x) + (3x+3)) = 0

(x-1) (x) x+1) + 3 (x+1) = 0

(x-1) (x+1) (x+3) = 0

x=1 x=-1 x=-3