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 a=t+1 and b=i:

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)