When f(x) = ax^3 - 6x^2 + bx - 5 is divided by x - 1, the remainder is -5. When f(x) is divided by x + 2, the remainder is 53. Find the ordered pair (a,b).
Its given that
When f(x) is divided by x-1 we get remainder
Now, when f(x) is divided by x+2 we get remainder
\(r' = -8a-2b-29\)
Subtracting eq (1) from (2)
From eq (1)
Hence the ordered pair (a,b) is (-7,-13).
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