Question

Using remainder theorem, find the remainder when x^3+3x^2+3x+1 is divided by [x−1/2].

Answer 1

According to Remainder Theorem

x + (-1/2) = 0

x = 1/2

Therefore if x³ + 3x² + 3x + 1 = 0 when we substitute x as 1/2 then x³ + 3x² + 3x + 1 is divisible by x + (-1/2)

Substituting Value of x as 1/2

(1/8) + (3/4) + (3/2) + 1

On Simplifying we get that it is equal to 27/8

which is ≠ 0

Therefore x + (-1/2) is not divisible by x³ + 3x² + 3x + 1

Answer 2

Answer

step by step explanation :

The root of x - (1/2) = 0 is 1/2.

p(1/2) = (1/2)3 + 3(1/2)2 + 3(1/2) + 1

= 1/8 + 3/4 + 3/2 + 1

= (1 + 6 + 12 + 8)/8 = 27/8

Hence by the remainder theorem, 27 / 8 is the remainder when x3 + 3x2 + 3x + 1 is divided by x.