HOW TO FIND GCD AND LCM OF TWO POLYNOMIALS

Key Concept

Practice Problems

Problem 1 :

Find the LCM and GCD of the following polynomials.

21x²y  and  35xy²

And also verify the relationship that the product of the polynomials is equal to the product of their LCM and GCD.

Solution :

Let f(x)  =  21x²y and g(x)  =  35xy²

f(x)  =  21x²y  =  3 ⋅ 7 ⋅ x² y 

g(x)  =  35xy² =  5 ⋅ 7 ⋅ x y² 

f(x) × g(x)  =  LCM × GCD

21x²y (35xy²)  =  (105 x² y²)(7xy)

  735x³y³  =  735x³y³ 

So, the relationship verified.

Problem 2 :

Find the LCM and GCD of the following polynomials.

(x³ −1)(x +1) and (x³ +1)

And also verify the relationship that the product of the polynomials is equal to the product of their LCM and GCD.

Solution :

Let f(x)  =  (x³ −1)(x +1) and g(x)  =  (x³ +1)

a³ -b³  =  (a-b)(a² + ab + b²)

f(x)  =  (x³ −1)(x +1)  =  (x - 1)(x² + x + 1)(x +1)

g(x)  =  (x³ +1) 

a³ + b³  =  (a+b)(a² - ab + b²)

g(x)  =  (x³ + 1)  =  (x + 1)(x² - x + 1)

f(x) × g(x)  =  LCM × GCD

(x³ −1)(x +1) ⋅ (x³ +1)  =  (x⁶ - y⁶) (x + 1)

(x³)² - (y³)²(x + 1)  =  (x⁶ - y⁶) (x + 1)

 (x⁶ - y⁶) (x + 1)  =   (x⁶ - y⁶) (x + 1)

So, the relationship verified.

Problem 3 :

Find the LCM and GCD of the following polynomials.

(x²y + xy²)  and  (x² + xy)

And also verify the relationship that the product of the polynomials is equal to the product of their LCM and GCD.

Solution :

Let f(x)  =  (x²y + xy²)  and g(x)  =  (x² + xy)

f(x)  =  (x²y + xy²)  =  xy (x + y)

g(x)  =  (x² + xy)  =  x(x + y)

f(x) × g(x)  =  LCM × GCD

xy (x + y) ⋅ x(x + y)  =  xy(x + y)  ⋅ x(x + y)

x²y(x + y)²  =  x²y(x + y)²

So, the relationship verified.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.