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)