Разложите квадратные трёхчлены на множители: 1) y^2+6y+9 2)x^2-2x-8 3)3x^2-7x+4 4)3x+10-x^2 5)-4x^2+7x 6)9a^2-25

1) y^2 + 6y + 9 = (y + 3)^2;

2)x^2 - 2x - 8 = 0

D = 4 - 4*(-8) = 36;

x1 = (2 - 6)/2 = -2;

x2 = (2 + 6)/2 = 4;

x^2 - 2x - 8 = (x - 4)(x + 2);

3)3x^2 - 7x + 4 = 0

D = 49 - 4*3*4 = 1;

x1 = (7 - 1)/2*3 = 1;

x2 = (7 + 1)/2*3 = 4/3;

3x^2 - 7x + 4 = 3(x - 1)(x - 4/3) = (x - 1)(3x - 4);

4) -x^2 + 3x + 10 = 0;

D = 9 - 4*(-1)*10 = 49;

x1 = (-3 - 7)/2*(-1) = 5;

x2 = (-3 + 7)/2*(-1) = -2;

3x + 10 - x^2 = -(x - 5)(x + 2) = (5 - x)(x + 2);

5)-4x^2 + 7x = x(-4x + 7) = x(7 - 4x);

6)9a^2 - 25 = (3a - 5)(3a + 5).