x(x - 19)(x - 1)
x^2-19x+90 (x-9) (x-10)
(x+7)(x+12)
(x - 10)(x - 9)
x2 - 19x + 60 = x2 - 15x - 4x + 60 = x(x - 15) - 4(x - 15) = (x - 15)(x - 4)
x(x - 19)(x - 1)
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: 3 plus or minus the square root of 19x = 7.358898943540674x = -1.358898943540674
x^2-19x+90 (x-9) (x-10)
(x+7)(x+12)
(x - 10)(x - 9)
(3x + 1)(x + 6)
(x + 12)(x + 7)
Factor as : (x+9)(x+10) using the first terms ( x terms) multiply to x2; the last terms multiply to 90; the sum of 9x + 10 x = 19x
x2 - 19x + 60 = x2 - 15x - 4x + 60 = x(x - 15) - 4(x - 15) = (x - 15)(x - 4)
19x
X2 + 19X - 42 = 0What two factors of - 42 add up to 19?(X - 2)(X + 21)----------------------FOIL and see the function reappear.X = 2X = - 21
use the quadratic formula since there isn't a factor of 60 that when added together equals 19 The above answer is wrong because 4 and 15 are such numbers. x2 + 19x + 60 = x2 + 4x + 15x + 60 = x(x + 4) + 15(x + 4) = (x + 4)(x + 15)