The Remainder Theorem




The remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor of f(x) if and only if f(r)=0.








1. Which of the following are factors of P(x) = x3 - 3x2 + x - 3:
















2. Which of the following are factors of P(x) = x4 + 10x3 + 8x2 - 8x + 9:












3. Which of the following are factors of P(x) = x45 + x44 - x23 - x22:












4. The polynomial P(x) = x3 + mx2 - 4x - 9 leaves a reminder of -8 when divided by x - 1. What is the value of m?
















5. Use the Remainder Theorem to find the remainder:

















6. Use the Remainder Theorem to find the remainder:




















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