How do you factor d^2 + 2d + 2?
1 Answer
Oct 10, 2016
This quadratic only factorises if you use Complex coefficients:
d^2+2d+2 = (d+1-i)(d+1+i)
Explanation:
Completing the square, we find:
d^2+2d+2 = (d+1)^2+1
This will be positive and therefore non-zero for any Real value of
If we allow Complex numbers then this can be factored as a difference of squares.
a^2-b^2 = (a-b)(a+b)
with
d^2+2d+2 = (d+1)^2+1
color(white)(d^2+2d+2) = (d+1)^2-i^2
color(white)(d^2+2d+2) = ((d+1)-i)((d+1)+i)
color(white)(d^2+2d+2) = (d+1-i)(d+1+i)
