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Exercise 3.3

1. Find the LCM and GCD for the following and verify that *f* (*x*)× *g* (*x*) = *LCM* ×*GCD*

(i) 21*x* 2*y*, 35*xy*2

(ii) (*x*3 − 1)(*x* + 1), (*x*3 + 1)

(iii) (*x*2*y* + *xy*2 ), (*x*2 + *xy*)

2. Find the LCM of each pair of the following polynomials

(i) *a *2* *+* *4*a *−12,* a *2* *−* *5*a *+* *6* *whose* GCD is a *–* *2

(ii) *x *4* *-* *27*a *3*x*,* *(*x *-* *3*a*)2* *whose* GCD *is* *(*x *-* *3*a*)

3. Find the GCD of each pair of the following polynomials

(i) 12(*x* 4 - *x* 3 ), 8(*x* 4 − 3*x* 3 + 2*x* 2 ) whose LCM is 24*x* 3(*x* - 1)(*x* - 2)

(ii) (*x* 3 + *y*3 ), (*x* 4 + *x* 2*y* 2 + *y*4 ) whose LCM is (*x* 3 + *y* 3 )(*x* 2 + *xy* + *y*2 )

4. Given the LCM and GCD of the two polynomials *p*(*x*) and *q*(*x*) find the unknown polynomial in the following table

Answers:

1. (i) 105*x* 2*y*2 , 7*xy*

(ii) (*x* − 1)(*x* + 1)(*x* 2 + *x* + 1)(*x* 2 − *x* + 1) , (*x* + 1)

(iii) *xy*(*x *+* y*)* *,* x *(*x *+* y*)

2.(i) (*a* + 6) (*a* - 2) (*a* - 3)

(ii) *x *(*x *−* *3*a *)2* *(*x *2 + 3*ax* + 9*a*2 )

3.(i) 4*x* 2 (*x* -1)

(ii) *x *2* *−* xy *+* y*2* *

4 (i)* *(*a *+* *2)(*a *−* *7)

(ii) *x *2* *+* xy *+* y*2

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10th Mathematics : UNIT 3 : Algebra : Exercise 3.3: Relationship between LCM and GCD | Problem Questions with Answer, Solution | Mathematics

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