Answer:
a = 3; b = -5
Step-by-step explanation:
x² -2x-3=(x-3)(x+1)
As it divides p(x); P(3) = 0 and P(-1) =0
P(x)= ax³ - 8x² + bx + 6
P(3) = 3³a - 8*9 + 3b + 6 =0
27a - 72 + 3b + 6 = 0
27a + 3b -66 =0
27a + 3b = 66 ------------------(i)
P(-1) = -a -8*(-1)² + b* (-1) + 6 = 0
-a - 8 -b + 6 = 0
-a - b -2 = 0
-a -b = 2 --------(ii)
(i) ------- 27a + 3b = 66
(ii)*3 -3a -3b = 6
Add 24a = 72
a = 72/24
a = 3
Substitute a value in (ii)
-3 - b= 2
-b = 2+3
-b= 5
b = -5
