Question

Find the reminder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.​

Answer 1

ANSWER

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

−5

​

p(

2

−5

​

)=(

2

−5

​

)

3

+3(

2

−5

​

)

2

+3(

2

−5

​

)+1

=

8

−125

​

+

4

75

​

−

2

15

​

+1

=

8

−125+150−60+8

​

=

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 is -27/8