Find the remainder when x³ + x² + x + 1 is divided by x - 1/2, by using remainder theorem.

Solution:

It is given that,

x³ + x² + x + 1 is divided by x - 1/2, by using the remainder theorem.

We have to find the remainder

x³ + x² + x + 1 --- (1)

Using remainder theorem, we get

⇒ x - 1/2 = 0

⇒ x = 1/2

Now, substitute the value of x in equation 1,

= (1/2)³ + (1/2)² + (1/2) + 1

= 1/8 + 1/4 + 1/2 + 1

So, LCM of 8, 4 and 2 is 8

= (1 + 2 + 4 + 8)/8

= 15/8

Therefore, the remainder is 15/8.

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Find the remainder when x³ + x² + x + 1 is divided by x - 1/2, by using remainder theorem.

Summary:

The remainder when x³ + x² + x + 1 is divided by x - 1/2, by using remainder theorem is 15/8.