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# Polynomial

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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).

Jun 2, 2022

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By remainder theorem, we get $$\begin{cases} f(1) = 5\\ f(2) = -53 \end{cases}$$.

Now, using the definition of f(x), we have a system of linear equations in a and b. Can you take it from here?

Jun 2, 2022