Find the complex factors of the quadratic trinomial x^2+8x+17

[x + (4-i) ][x + (4+i) ]

Step-by-step 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) ]