Question

Answer this question with process

Answer 1

Answer:

By remainder theorem

x+1=0

x=−1

p(x)=x^3

+3x^2

−3x−1p(−1)

=(−1)^3+3(−1)^2−3(−1)−1

=−1+3(1)+3−1

=−1+3+3−1

=6−2 =4

Thus remainder is 4

ii)

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= 5/2

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+ 475− 215 +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 +3x2+3x+1 is divided by 5+2x.

hopefully this will help you