Answer:
steps below
Step-by-step explanation:
x⁶ - 7x³ - 8 = (x⁶ + x³) - (8x³ + 8)
= x³ (x³+1)-8(x³+1)
= (x³ - 2³)(x³ + 1)
= (x-2)(x²+2x+4)(x+1)(x²-x+1)
(x-2)(x²+2x+4)(x+1)(x²-x+1) = 0
x= -1 or x = 2 ... roots
or x²+2x+4=0 or x²-x+1=0
x²+2x+4=0
x = (-2±√4-16)/2 = -1 ± √3 i ... complex roots
x²-x+1=0
x = (1±√1-4)/2 = 1/2 ± (√3)i / 2 ... complex roots
b) P(x) = x⁶ - 7x³ - 8
= (x-2)(x²+2x+4)(x+1)(x²-x+1)
= (x+1)(x-2)(x-(-1 + √3 i))(x-(-1 - √3 i)(x-(1/2 + (√3)i / 2))(x-(1/2 - (√3)i / 2))
