Question

Find the remainder when x3+3x2+3x+1 is divided by.. x-1/2​

Answer 1

ANSWER :–

GIVEN :–

A FUNCTION X³ + 3X² + 3X + 1 = 0 IS DIVIDED BY ( X - ½ )

TO FIND :–

REMAINDER AFTER DIVIDE.

SOLUTION :–

▪︎ LET'S USING REMAINDER THEOREM –

SO , THAT PUT X = ½ IN GIVEN FUNCTION –

=> REMAINDER = (½)³ + 3 (½)² + 3(½) + 1

=> REMAINDER = ⅛ + 3(¼) + 3(½) + 1

=> REMAINDER = (1/8) + (3/4) + (3/2) + 1

=> REMAINDER = 27/8

Answer 2

Answer:

$\frac{27}{8}$

Step-by-step explanation:

Let p(x) = x³ + 3x² + 3x + 1

$x-\frac{1}{2}=0$  ⇒ $x=\frac{1}{2}$

∴ Remainder

$= (\frac{1}{2} )^{3} + 3 (\frac{1}{2} )^{2} + 3(\frac{1}{2}) + 1\\\\= \frac{1}{8} + \frac{3}{4} +\frac{3}{2}+ 1\\= \frac{27}{8}$

∴ The Remainder is $\frac{27}{8}.$