How do you factor completely: #x^2 − 2x + 5#?

1 Answer
Jul 15, 2015

Answer:

#x^2-2x+5 = (x-1+2i)(x-1-2i)#
#color(white)("XXXX")#(there are no Real factors for the given expression)

Explanation:

Write the expression as an equation with the expression equal to zero.
#color(white)("XXXX")##x^2-2x+5 = 0#
Us the quadratic formula to determine the roots:
#color(white)("XXXX")##(-b+-sqrt(b^2-4ac))/(2a)#
becomes
#color(white)("XXXX")##1+-2i#

That is
#color(white)("XXXX")##(x - (1+2i))*(x-(1-2i)) = 0#

So
#color(white)("XXXX")##(x-1-2i) and (x-1+2i)# are factors of the the given expression.