Question

Find the remainder when x3+3x2+3x+1 is divided by. i) x+1
ii) x-1/2
iii) x
iv) x+pi
v) 5+2x​

Answer 1

Answer with Step-by-step explanation:

( i ) x + 1

Dividing x3 + 3x2 + 3x + 1 (Dividend)  by x + 1 (Divisor)

Step 1 :

Put

Divisor = 0

X + 1 = 0

X = -1

Step 2 : Let p ( x ) = x3 + 3x2 + 3x + 1

Putting x = -1

p ( -1 ) = ( -1 )^ 3 + 3 ( -1 ) ^2 + 3 ( -1 ) + 1 = -1 + 3-3 + 1

= 0 Thus , remainder = P ( -1 ) = 0

(ii) x-1/2

Dividing x^3 + 3x^2 + 3x + 1 (Dividend)  by x -1/3 (Divisor)

Step 1 :

Put Divisor = 0

X - 1 /2 = 0

X = 1/2

Step 2 : Let p ( x ) = x3 + 3x2 + 3x + 1 Putting x = } PC- + 3 ) +3 ) +1 = + 3 ( ) + +1 1 = - + - + 8 4 - + 1 1 + 3 ( 2 ) + 3 ( 4 ) +1 ( 8 ) 8 = 1+ 6 + 1 2 + 8 8 8