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Answer :
Final answer:
Substituting x=5 into the polynomial x³ - x² + 3x - 1 due to the Remainder Theorem, we calculate the function to be 114. The remainder when x³ - x² + 3x - 1 is divided by x-5 is 114.
Explanation:
When we divide polynomial x³ - x² + 3x - 1 by x-5 to find the remainder, we utilize the Remainder Theorem. According to this theorem, if you are dividing the polynomial f(x) by x - k, the remainder is the same as evaluating the function f(x) at x=k. In this case, substitute x=5 into the polynomial.
The function f(x) = x³ - x² + 3x - 1 becomes f(5)= (5)³ - (5)² + 3(5) -1 = 125 - 25 + 15 -1 = 114
So, the remainder when x³ - x² + 3x - 1 is divided by x-5 is 114.
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