GCD Worksheet Solution3





In this page gcd worksheet solution3 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.

(5) Find the GCD of the following

2 x² - x - 1 , 4 x² + 8 x + 3

Solution:

2 x² - x - 1 = (2 x + 1) (x - 1)

4 x² + 8 x + 3 = (2x + 3) (2x + 1)

Therefore the greatest common divisor = (2 x + 1)


(11) Find the GCD of the following

x² - x - 2 , x² + x - 6 , 3 x² - 13 x + 14

Solution:

x² - x - 2 = (x + 1) (x - 2)

x² + x - 6 = (x + 3) (x - 2)

3 x² - 13 x + 14 = (x - 2) (3 x - 7)

Therefore the greatest common divisor = (x - 2)


(12) Find the GCD of the following

x³ - x² + x - 1 , x⁴ - 1

Solution:

x³ - x² + x - 1 =

                    = (x - 1) (x² + 1)

           x⁴ - 1  = (x²)² -  (1²)²

                    = (x² + 1) (x² - 1)

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

Therefore the greatest common divisor = (x - 1) (x² + 1)               


(13) Find the GCD of the following

24 (6 x⁴ - x³ - 2 x²) , 20 (2 x⁶ + 3 x⁵ + x⁴)

24 (6 x⁴ - x³ - 2 x²) = 2 x 3 x 2 x 2 x x² (6x² - x - 2)

                           = 2 x 3 x 2 x 2 x x² (3x - 2) (2x + 1)

20 (2 x⁶ + 3 x⁵ + x⁴)  = 5 x 2 x 2 x x⁴ (2 x² + 3 x + 1)

                           = 5 x 2 x 2 xx x² (x + 1) (2x + 1)

Therefore the greatest common divisor =  2 x 2 xx (2x + 1)

                                                     = 4x² (2x + 1)

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