What is the remainder when x³ - x + 1 is divided by 2x - 1?

Solution:

It is given that,

x³ - x + 1 is divided by 2x - 1, by using the remainder theorem.

We have to find the remainder. According to the remainder theorem, if f(x) is divided by (x-a) then f(a) gives the remainder.

f(x)= x³ - x + 1 --- (1)

here the divisor is 2x - 1 = 0

⇒ x = 1/2

Now, substitute the value of x in equation 1,

= (1/2)³ - 1/2 + 1

= 1/8 - 1/2 + 1

So, LCM of 8 and 2 is 8

= (1 - 4 + 8)/8

= 5/8

Therefore, the remainder is 5/8.

---

What is the remainder when x³ - x + 1 is divided by 2x - 1?

Summary:

The remainder when x³ - x + 1 is divided by 2x - 1, by using remainder theorem is 5/8.