Ncert Solutions For Class 9 Maths Ex 2.3

Ncert Solutions For Class 9 Maths Chapter 2 Ex 2.3

Q.1.Find the remainder when x3+3x2+3x+1 is divided by

(i) x+1

Answer:

x+1=0x=1 Remainder=p(1)=(1)3+3(1)2+3(1)+1=1+33+1=0

 

(ii) x12

Answer:

x12=0x=12 Remainder(12)3+3(12)2+3(12)+1=18+34+32+1=278

 

(iii) x

Answer:

Remainder=(0)3+3(0)2+3(0)+1=1

 

(iv) x+π

Answer:

x+π=0x=π Remainder=(π)3+3(π)2+3(π)+1=π3+3π23π+1

 

(v) 5+2x

Answer:

5+2x=02x=5x=52 Remainder=(52)3+3(52)2+3(52)+1=1258+754152+1=278

 

Q.2.Find the remainder when x3ax2+6xa is divided by x-a.

Answer:

Let p(x)=x3ax2+6xaxa=0

x=a Remainder=(a)2a(a2)+6(a)a=a3a3+6aa=5a

 

Q.3.Check whether 7+3x is a factor of 3x3+7x.

Answer:

7+3x=03x=7 only if 7+3x divides 3x3+7x leaving no reaminder.

Let p(x)=3x3+7x

7+3x=03x=7x=73 Remainder=3(73)3+7(73)=3439493=49090

7+3x is not a factor of 3x3+7x