# What is the remainder when x^{3} - x + 1 is divided by 2x - 1?

**Solution:**

It is given that,

x^{3} - 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)= x^{3} - 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 x^{3} - x + 1 is divided by 2x - 1?

**Summary:**

The remainder when x^{3} - x + 1 is divided by 2x - 1, by using remainder theorem is 5/8.

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