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

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