High School

Find the remainder when the polynomial [tex]x^3 - x^2 + 3x - 1[/tex] is divided by [tex]x - 5[/tex].

A. -114
B. 14
C. 114
D. 1014

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.

Learn more about Remainder Theorem here:

https://brainly.com/question/13547729

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