# FINDING GCD OF POLYNOMIALS EXAMPLES

## About "Finding GCD of Polynomials Examples"

Finding GCD of Polynomials Examples :

Here we are going to see some example problems on finding GCD of polynomials.

To find the GCD by Factorisation

(i) Each expression is to be resolved into factors fi rst.

(ii) Th e product of factors having the highest common powers in those factors will be the GCD.

(iii) If the expression have numerical coefficient, find their GCD separately and then prefix it as a coefficient to the GCD for the given expressions.

## Finding GCD of Polynomials Examples - Practice questions

Question 1 :

Find the GCD for the following:

(i)  p5, p11, p9

Solution :

The minimum term of given terms,

=  p5

Hence the required GCD is p5

(ii)  4x3, y3, z3

Solution :

There is not common term for the given three terms.

Hence GCD is 1.

(iii)  9 abc3, 15 abc4

Solution :

9 abc=  32 a⋅  b⋅ c3

15 abc=  3 ⋅ a⋅  b⋅ c4

G.C.D  =  3a2 bc3

(iv)  64x8, 240x6

Solution : 64  =  2 and 240  =  24 ⋅ 5 ⋅ 3

G.C.D  =  24 x  =  16x6

Hence the required G.C.D is 16x6.

(v)  ab2c3, a2b3c, a3bc2

Solution :

ab2c3, a2b3c, a3bc2

Hence GCD is abc.

(vi)  35 x5 y3 z4, 49 xy z3, 14 x yz2

Solution :

35  = ⋅ 7

49  =  72

14  =  2 ⋅ 7

=  7 xy z3

Hence the GCD is 7 xy z3.

(vii)  25ab3c, 100 a2bc, 125 ab

Solution :

25ab3c  =  52ab3c

100 a2bc  = 22 ⋅ 52 a2bc

125 ab  =  53 ab

GCD  =  52 ab  =  25ab

Hence GCD is 25ab.

(viii)  3 abc, 5 xyz, 7 pqr

Solution :

There is no common terms, hence the GCD is 1.

Question 2 :

Find the GCD of the following:

(i) (2x +5), (5x +2)

Solution :

The given polynomials are different, since they have no common terms.

G.C.D is 1.

(ii)  am + 1, am + 2, am + 3

Solution :

The common term is am + 1

Hence GCD is am + 1.

(iii)  2a2 + a, 4a2 - 1

Solution :

2a2 + a  =  a(2a + 1)

4a2 - 1  =  (2a)2 - 12

=  (2a + 1)(2a - 1)

Hence GCD is 2a + 1.

(iv)  3a2, 5b3, 7c4

Solution :

Hence the GCD is 1.

(v)  x4 - 1, x2 - 1

Solution :

x4 - 1  =  (x2)2 - (12)2

=  (x2 + 1)(x2 - 1)

=  (x2 + 1)(x + 1)(x - 1)

x2 - 1  =  (x + 1) (x - 1)

Hence GCD is (x + 1) and (x - 1).

(vi)  a3 - 9ax2, (a - 3x)2

Solution :

a3 - 9ax =  a(a2 - 9x2)

=  a(a2 - (3x)2)

=  a (a + 3x) (a - 3x)

(a - 3x)2  =  (a  - 3x)(a - 3x)

Hence the GCD is (a  - 3x). After having gone through the stuff given above, we hope that the students would have understood, "Finding GCD of Polynomials Examples"

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