Find the values of a and b so that the polynomial x^3 -10x^2 +ax +b is exactly divisible by x-1 as well as x-2

a = 23, b = - 14

Step-by-step 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

30

step-by-step explanation:

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a and c

step-by-step explanation: