How do you factor x^2 - 2x + 5?
Oh, I see, thanks so much!
x^2 - 2x + 5=
= x^2 - 2x + 4+1
=[x-2]^2+1
x^2-2x+5
=x^2-2+1+4
=(x-1)^2 +4
You apply the square rule. (.5b)^2
x^2-2x+5 b=2 --- (.5(2))^2 =1
x^2-2x+1+5-1
(x-1)(x-1)+4
(x-1)^2 +4
The factors of 5 are 1 and 5 or -1 and -5; neither of these sum to -2, so you have to use the quadratic equation.
(-b ± sqrt(b^2 - 4ac))/2a
(2 ± sqrt(4 - 20))/2
(2 ± 4i)/2
1 ± 2i
Thus, factored, it is (x - 1 + 2i)(x - 1 - 2i).
Comments
x^2 - 2x + 5=
= x^2 - 2x + 4+1
=[x-2]^2+1
x^2-2x+5
=x^2-2+1+4
=(x-1)^2 +4
You apply the square rule. (.5b)^2
x^2-2x+5 b=2 --- (.5(2))^2 =1
x^2-2x+1+5-1
(x-1)(x-1)+4
(x-1)^2 +4
The factors of 5 are 1 and 5 or -1 and -5; neither of these sum to -2, so you have to use the quadratic equation.
(-b ± sqrt(b^2 - 4ac))/2a
(2 ± sqrt(4 - 20))/2
(2 ± 4i)/2
1 ± 2i
Thus, factored, it is (x - 1 + 2i)(x - 1 - 2i).