GCD Worksheet Solution4





In this page gcd worksheet solution4 we are going to see solution of some question with clear explanation.

To find the greatest common divisor of the given numbers or for algebraic expressions we have to follow the steps:

Step 1: List the prime factors of each of the given number. For algebraic expression we have to find factors of them.

Step 2: List the common factors of the given numbers or common factors.

Step 3: Multiply those common factors.

(14) Find the GCD of the following

(a - 1)⁵ (a + 3)² , (a - 2)² (a - 1)³ (a + 3)⁴

Solution:

(a - 1)⁵ (a + 3)² =  (a - 1)³ (a - 1)² (a + 3)²

(a - 2)² (a - 1)³ (a + 3)⁴ = (a - 2)² (a - 1)³ (a + 3)² (a + 3)²

Therefore the greatest common divisor = (a - 1)³ (a + 3)²


(15) Find the GCD of the following pairs of polynomials using division algorithm

Solution:

f (x) = x³ - 9 x² + 23 x - 15 

g (x) = 4 x² - 16 x + 12

       = 4 (x² - 4 x + 3)

Therefore GCD is x - 5


(16) Find the GCD of the following pairs of polynomials using division algorithm

3 x³ + 18 x² + 33 x + 18 ,  3 x² + 13 x + 10

Solution:

f (x) = 3 x³ + 18 x² + 33 x + 18

g (x) = 3 x² + 13 x + 10

We are not taking any number from f (x).

Since we are not getting zero we have to do this long division once again.Now we are taking 4/3 as common from the remainder. So that we are getting (4/3)(x+1)

Therefore G.C.D is x + 1


(17) Find the GCD of the following pairs of polynomials using division algorithm

2 x³ + 2 x² + 2 x + 2 ,  6 x³ + 12 x² + 6 x + 12

Solution:

f (x) = 2 (x³ + x² + x + 1)

g (x) = 6 (x³ + 2 x² + x + 2)

We are taking 2 from f (x) and 6 from g (x)

Since we are not getting zero we have to do this long division once again

Therefore GCD is 2 (x² + 1)


(18) Find the GCD of the following pairs of polynomials using division algorithm

x³ - 3 x² + 4 x - 12 , x⁴ + x³ + 4 x² + 4 x

Solution:

f (x) = x³ - 3 x² + 4 x - 12

g (x) = x (x³ + x² + 4 x + 4)

We are taking x from g (x).

Since we are not getting zero we have to do this long division once again

Therefore GCD is (x² + 4)

gcd worksheet solution4  gcd worksheet solution4