Answer: 5
Step-by-step explanation:
p(x) = x³ - 3x² + 2x + 5 p(a) = p(b) = p(c) = 0
0 = x³ - 3x² + 2x + 5
0 = (x - a)(x - b)(x - c)
= x³ − (a + b + c)x² + (ab + bc + ca)x - abc
↓ ↓ ↓
-3 2 5
-(a + b + c) = -3
a + b + c = 3
ab + bc + ca = 2
-(abc) = 5
abc = -5
(2 - a) (2 - b) (2 - c)
= 8 - 4(a + b + c) + 2(ab + bc + ca) - abc
= 8 - 4(3) + 2(2) -(-5)
= 8 - 12 + 4 + 5
= 5
