**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.

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

(i) 21x^{2}y, 35xy^{2 }Solution

(ii) (x^{3} −1)(x +1), (x^{3} +1)^{ }Solution

(iii) (x^{2}y + xy^{2}), (x^{2} + xy)^{ }Solution

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

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

(ii) x ^{4} -27a^{3}x, (x -3a)^{2} whose GCD is (x -3a) Solution

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

(i) 12(x^{4} -x^{3}), 8(x^{4} −3x^{3} +2x^{2}) whose LCM is 24x^{3}(x -1)(x -2) Solution

(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}) 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 = a GCD = a - 7 p(x) = a find q(x) |
(ii) LCM = (x (x GCD = (x q(x) = (x find p(x) |

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