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 **x **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 **x **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

- Back to worksheet
- GCD worksheet
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- Elimination method worksheet
- Cross multiplication method worksheet
- Equation from roots worksheet
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