9 - x2 will factor into (3 - x)(3 + x)
x2-9x = x(x-9)
x2-49 = (x-7)(x+7)
X2 - 16(X - 4)(X + 4)============X2 + 16===========not factorable in real numbers
x2 + 2x - 3 = (x + 3)(x - 1)
-x2 + x + 42 = -[x2 - x - 42] = -[x2 - 7x + 6x - 42] = -[x*(x - 7) + 6*(x - 7)] = -(x - 7)*(x + 6)
(x + 6) (x - 7)
(x - 7)(x + 6)
(x - 6)(x - 7)
It is: (x+7)(x-6) when factored
(x + 7)(x - 6)
44
44
(x - 6)(x - 7)
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
-x2 + x + 42= -x2 + 7x - 6x + 42= 7x - x2 + 42 - 6x= x(7 - x) + 6(7 - x)= (7 - x)(x + 6)
x4 + x2 - 42 Let x2 = t, so that x4 = t2 t2 + t - 42 since -42 = 7(-6) and 7 + (-6) = 1, then t2 + t - 42 = (t - 6)(t + 7) = (x2 - 6)(x2 + 7) By replacing t with x2. So we have, x4 + x2 - 42 = (x2 - 6)(x2 + 7) = [x2 - (square root of 6)2](x2 + 7) = (x - sq. root of 6 )(x + sq. root of 6)(x2 + 7)