Question

When x${}^3$ - 5x${}^2$ + 3x + 1 is divided by x - 1, find the remainder.

• A. \N

Answer 1

The correct option is A \N
Given: Dividend = x${}^3$ - 5x${}^2$ + 3x + 1, divisor = x - 1

Let f(x) = x${}^3$ - 5x${}^2$ + 3x + 1 and g(x) = x - 1

We know that if f(x) is divided by x - a, then the remainder is f(a).

So, when f(x) = x${}^3$ - 5x${}^2$ + 3x + 1 is divided by x - 1, then remainder will be f(1).

f(1) = 1${}^3$ - 5(1)${}^2$ + 3(1) + 1
f(1) = 1 - 5 + 3 + 1
f(1) = 0
Remainder = 0