How do you factor #x^2 + 12x + 31# by completing the square?
1 Answer
Jun 24, 2016
Complete the square and use the difference of squares identity to find:
#x^2+12x+31=(x+6-sqrt(5))(x+6+sqrt(5))#
Explanation:
We will also use the difference of squares identity:
#a^2-b^2 = (a-b)(a+b)#
with
#x^2+12x+31#
#=x^2+2(6x)+36-5#
#=(x+6)^2-(sqrt(5))^2#
#=((x+6)-sqrt(5))((x+6)+sqrt(5))#
#=(x+6-sqrt(5))(x+6+sqrt(5))#
