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


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


(ii) x12


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


(iii) x




(iv) x+π


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


(v) 5+2x


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.


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.


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


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