Answer:
a = 23, b = - 14
Explanation:
If the polynomial is divisible by (x - 1) then f(1) = 0
f(x) = x³ - 10x² + ax + b
f(1) = 1³ - 10(1)² + a + b = 0, that is
1 - 10 + a + b = 0, hence
a + b = 9 → (1)
Similarly if (x - 2) is a factor then f(2) = 0
f(2) = 2³ - 10(2)² + 2a + b = 0, that is
8 - 40 + 2a + b = 0, hence
2a + b = 32 → (2)
Subtract (1) from (2)
a = 23
Substitute a = 23 into (1)
23 + b = 9 ⇒ b = 9 - 23 = - 14