LCM and GCD Solution2





In this page lcm and gcd solution2 we are going to see solution of some questions with detailed explanation.

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

(iv) 2 x³ - 3 x² - 9 x + 5 , 2 x⁴ - x³ - 10 x² - 11 x + 8 whose GCD is 2 x - 1

Solution:

 L.C.M x G.C.D = f (x) x g (x)

 f (x) = 2 x³ - 3 x² - 9 x + 5

 g (x) = 2 x⁴ - x³ - 10 x² - 11 x + 8

 G.C.D = 2 x - 1

 L.C.M = [ f (x) x g (x) ]/G.C.D

          = [ (2 x³ - 3 x² - 9 x + 5) (2 x⁴ - x³ - 10 x² - 11 x + 8)]/(2 x - 1)

To simplify this we have to use long division.

          = (x² - x - 5) (2 x⁴ - x³ - 10 x² - 11 x + 8)


(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:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = (x + 1)² (x + 2)²

 G.C.D = (x + 1) (x + 2)

 p (x) = (x + 1)² (x + 2)

  q (x) = [ L.C.M G.C.D ]/p(x)

         = [ (x + 1)² (x + 2)²  (x + 1) (x + 2) ]/(x + 1)² (x + 2)

    q (x) = (x + 2)²  (x + 1)   


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

Solution:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = (4 x + 5)³ (3 x - 7)³

 G.C.D = (4 x + 5) (3 x - 7)²

 p (x) = (4 x + 5)³ (3 x - 7)²

  q (x) = [ L.C.M G.C.D ]/p (x)

         = [ (4 x + 5)³ (3 x - 7)³ (4 x + 5) (3 x - 7)² ]/(4 x + 5)³ (3 x - 7)²

  q (x) = (3 x - 7)³ (4 x + 5)

lcm and gcd solution2  lcm and gcd solution2