**Lcm and gcd worksheet :**

Here we are going to see some practice questions. For each question we have solution with detailed explanation.

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

(i) x² - 5 x + 6 , x² + 4 x - 12 whose G.C.D is (x - 2) Solution

(ii) x⁴ + 3 x³ + 6 x² + 5 x + 3 , x⁴ + 2 x² + x + 2 whose G.C.D is x² + x + 1 Solution

(iii) 2 x³ + 15 x² + 2 x - 35 , x⁴ + 8 x² + 4 x - 21 whose G.C.D is x + 7 Solution

(iv) 2 x³ - 3 x² - 9 x + 5 , 2 x⁴ - x³ - 10 x² - 11 x + 8

whose G.C.D is 2 x - 1 Solution

(2) Find the other polynomial q (x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(i) (x + 1)² (x + 2)² , (x + 1) (x + 2) , (x + 1)² (x + 2) Solution

(ii) (4 x + 5)³ (3 x - 7)³ , (4 x + 5) (3 x - 7)² , (4 x + 5)³ (3 x - 7)³ Solution

(iii) (x⁴ - y⁴) (x⁴ + x²y² + y⁴) , x² - y² , x⁴ - y⁴ Solution

(iv) (x³ - 4 x) (5 x + 1) , (5 x² + x) , (5 x³ - 9 x² - 2x) Solution

(v) (x - 1) (x - 2) (x² - 3 x + 3) , (x - 1) , (x³ - 4 x² + 6 x - 3) Solution

(vi) 2 (x + 1) (x² - 4) , (x + 1), (x + 1) (x - 2) Solution

- GCD worksheet
- LCM worksheet
- Elimination method worksheet
- Cross multiplication method worksheet
- Equation from roots worksheet
- Synthetic division worksheet
- Factorization worksheet
- Simplifying rational expression

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