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Let be a polynomial such that f(0) = 4, f(-1) = 5, and f(2) = 10. Find the remainder when f(x) is divided by x(x + 1)(x - 2).

 May 7, 2022
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Since the divisor is cubic, the remainder is at most quadratic, so we may let ax^2 + bx + c be the remainder.

 

By "remainder theorem", we have \(\begin{cases}c = 4\\a - b + c = 5\\4a + 2b + c = 10\end{cases}\). (The details are similar to this solution here: https://web2.0calc.com/questions/polynomial_92348#r1)

 

The value of c is already known. You can solve for a, b here to know the coefficients of the remainder. After you get the values of all of a, b, c, the remainder will be known.

 May 8, 2022

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