All three of the questions are factoring by grouping.

Question

#23) x^2-ix+6=0

#41) Which expression represents 625p^4-16 when factored completely over the complex numbers?

#49) x^3-2x^2+9x-18=0

Answer 1

(1)

A = 1, B = -i C = 6

B^2 - 4ac = (-i)^2 - 4(1)(6)

= -1 - 24

= -25

x = [i +or- sqrt(-25)] / 2

= [ i +or- 5i] / 2

x = 3i or x = -2i

check:

(3i)^2 -i(3i)+6 =-9 +3+6=0

(-2i)^2 -i(-2i) + 6 = -4 -2+6 = 0

(2)

[25p^2 + 4] [25p^2 - 4] =

[25p^2 + 4] [5p+2][5p-2]

[5p + 2i][5p-2i][5p+2][5p-2]

(3) x^2(x-2) + 9*(x-2) =

(x-2)(x^2+ 9)