# FINDING LCM AND HCF OF POLYNOMIALS AND RELATIONSHIP WORKSHEET

Finding LCM and HCF of Polynomials and Relationship Worksheet :

Here we are going to see some practice questions on finding HCF and LCM.

To find GCD or LCM, first we have to find the factors of the given expression or polynomial.

• If we have coefficients of x or y term, then we have to decompose the coefficients as much as possible.
• If we have quadratic or cubic expression, then we have to factorize using suitable algebraic identities.
• To get GCD, multiply the common factors
• To get LCM, multiply highest factors.

## Finding LCM and HCF of Polynomials and Relationship Worksheet - Questions

(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)

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

(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 + 70GCD  =  a - 7p(x)  =  a2 −12a + 35find q(x) (ii)LCM = (x2 +y2)(x4 +x2y2+y4)GCD  =  (x2 -y2) (x4 −y4)q(x)  =  (x2 +y2 −xy)find p(x)

After having gone through the stuff given above, we hope that the students would have understood, how to find HCF and LCM of polynomials.

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