8/16/2019 NCERT Class 9 ch-2 examples
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Example 1 : Find the degree of each of the polynomials given
below:
(i) x5 – x4 + 3 (ii) 2 – y2 – y3 +
2 y (iii) 2
Example 2 : Find the val!e of each of the following polynomials
at the indicated val!e
of variables:
(i) p( x) " 5 x2 – 3 x + # at x "
$%(ii) q( y) " 3 y3 – 4 y + (s&!are root of
$$) at y " 2%
(iii) p(t ) " 4t 4 + 5t 3 – t 2 +
' at t " a%Example 3 : hec whether –2 and 2 are *eroes of the
polynomial x + 2%
Example 4 : Find a *ero of the polynomial p( x) "
2 x + $%
Example 5 : erify whether 2 and , are *eroes of the
polynomial x2 – 2 x%
Example 6 : -ivide p( x) by g ( x).
where p( x) " x + 3 x2 – $
and g ( x) " $ + x%
Example 7 : -ivide the polynomial 3 x4 –
4 x3 – 3 x –$ by x – $%
Example 8 : Find the remainder obtained on
dividing p( x) " x3 + $ by x + $%
Example 9 : Find the remainder when x4 + x3 –
2 x2 + x + $ is divided by x – $%
Example 10 : hec whether the polynomial q(t ) " 4t 3 +
4t 2 – t – $ is a m!ltiple of 2t +$%
Example 11 : /0amine whether x + 2 is a factor of x3 +
3 x2 + 5 x + ' and of 2 x + 4%
Example 12 : Find the val!e of k . if x – $ is a
factor of 4 x3 + 3 x2 – 4 x + k %
Example 13 : Factorise ' x2 + $# x + 5 by splitting
the middle term. and by !sing the
Factor 1heorem%
Example 14 : Factorise y2 – 5 y + ' by !sing the
Factor 1heorem%
Example 15 : Factorise x3 – 23 x2 +
$42 x – $2,%
Example 16 : Find the following prod!cts !sing appropriate
identities:(i) ( x + 3) ( x + 3) (ii) ( x – 3)
( x + 5)
Example 17 : /val!ate $,5 $,' witho!t m!ltiplying directly%
Example 18 : Factorise:
(i) 4a2 + #,ab + 25b2 (ii) 254 x2 − y2
Example 19 : rite (3a + 4b + 5c)2 in e0panded form%
Example 20 : /0pand (4a – 2b – 3c)2%
Example 21 : Factorise 4 x2 + y2
+ z 2 – 4 xy – 2 yz +
4 xz %
Example 22 : rite the following c!bes in the e0panded form:
(i) (3a + 4b)3 (ii) (5 p – 3q)3
Example 23 : /val!ate each of the following !sing s!itable
identities:
(i) ($,4)3 (ii) ()3Example 24 : Factorise x3 + 2# y3
+ 3' x2 y + 54 xy2
Example 25 : Factorise : x3 + y3 +
2# z 3 – $ xyz
