How do you factor the trinomial #t^2 + 2t + 2#?
1 Answer
Dec 10, 2015
Complete the square then use the difference of squares identity to find:
#t^2+2t+2 = (t+1-i)(t+1+i)#
Explanation:
The difference of squares identity may be written:
#a^2-b^2 = (a-b)(a+b)#
Complete the square then use this identity with
#t^2+2t+2#
#= t^2+2t+1+1#
#= (t+1)^2+1#
#= (t+1)^2-i^2#
#= ((t+1)-i)((t+1)+i)#
#= (t+1-i)(t+1+i)#
