Answer:
[x+(4-i)][x+(4+i)]
Explanation:
Complete the square then regroup the first two terms. Add and subtract: (b/2)^2=(8/2)^2=16
x^2+8x+17=(x^2+8x)+17
=(x^2+8x+16)+17-16
=(x+4)^2+1 create a difference of squares using i^2= -1
=(x+4)^2 - (-1)
=(x+4)^2 - i^2 use the difference of two squares identity
=[(x+4) - i][(x+4)+i]
=[x+(4-i)][x+(4+i)]