FINDING LCM AND HCF OF POLYNOMIALS AND RELATIONSHIP WORKSHEET

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

(i) 21x2y, 35xy2            Solution

(ii)  (x3 −1)(x +1), (x3 +1)       Solution

(iii) (x2y + xy2), (x2 + xy)         Solution

(2)  Find the LCM of each pair of the following polynomials

(i) a2 + 4a −12, a2 −5a + 6 whose GCD is a -2     Solution

(ii) x 4 -27a3x, (x -3a)2 whose GCD is (x -3a)    Solution

(3)  Find the GCD of each pair of the following polynomials

(i) 12(x4 -x3), 8(x4 −3x3 +2x2) whose LCM is 24x3(x -1)(x -2)       Solution

(ii) (x3 + y3), (x4 + x2y2 + y4) whose LCM is (x3 + y3)(x2 + xy + y2)        Solution

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

(i)

LCM

= a3 −10a2 +11a + 70

GCD  =  a - 7

p(x)  =  a2 −12a + 35

find q(x)  

Solution

(ii)

LCM = (x2 +y2)

(x4 +x2y2+y4)

GCD  =  (x2 -y2) (x4 −y4)

q(x)  =  (x2 +y2 −xy)

find p(x)

Solution

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