Question

find the remainder when x ³ + 3 X ² + 3 X + 1 is divided by 2 X + 5​

Answer 1

Dividing x 3+3x 2+3x+1 by 5+2x

So, x 3+3x 2+3x+1 is dividend and 5+2x is divisor.

Put, 5+2x=0

∴ x= 2−5

Let p(x)=x 3+3x 2+3x+1

Putting x= 2−5p( 2−5)=(2−5 ) 3+3( 2−5 )

2 +3( 2−5)+1= 8−125+ 475 −215 +1 =

8−125+150− = 8-27

Thus, reminder of p(

2

−5

)=

8

−27

.

∴ We will get reminder as

8

−27

when x

3

+3x

2

+3x+1 is divided by 5+2x.

Answer 2

Answer:

The remainder of the given division is -27/8.