RD Sharma Solutions for Class 8 Chapter - 7 Factorization Exercise 7.1

Our expert team has designed the solutions for RD Sharma Class 8 Maths Chapter 7 to help students prepare for their exams at ease. RD Sharma Solutions is one of the best reference material for CBSE students. Learners can download the pdf from the links provided below. Experts suggest students practice the solutions many numbers of times to yield good results in their exams. In Exercise 7.1 of Chapter 7 Factorization, we shall discuss the basic definitions for factors, factorization and we also find the common factors and greatest common factor of the monomial.

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Find the greatest common factor (GCF/HCF) of the following polynomials: (1-14)

1. 2x² and 12x²

Solution:

We know that the numerical coefficients of given numerical are 2 and 12

The greatest common factor of 2 and 12 is 2

The common literals appearing in given monomial is x

The smallest power of x in two monomials is 2

The monomial of common literals with smallest power is x²

∴ The greatest common factor = 2x²

2. 6x³y and 18x²y³

Solution:

We know that the numerical coefficients of given numerical are 6 and18

The greatest common factor of 6 and 18 is 6

Common literals appearing in given numerical are x and y

Smallest power of x in three monomial is 2

Smallest power of y in three monomial is 1

Monomial of common literals with smallest power is x²y

∴ The greatest common factor = 6x²y

3. 7x, 21x² and 14xy²

Solution:

We know that the numerical coefficients of given numerical are 7, 21 and 14

Greatest common factor of 7, 21 and 14 is 7

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 1

Smallest power of y in three monomials is 0

Monomials of common literals with smallest power is x

∴ The greatest common factor = 7x

4. 42x²yz and 63x³y²z³

Solution:

We know that the numerical coefficients of given numerical are 42 and 63.

Greatest common factor of 42, 63 is 21.

Common literals appearing in given numerical are x, y and z

Smallest power of x in two monomials is 2

Smallest power of y in two monomials is 1

Smallest power of z in two monomials is 1

Monomials of common literals with smallest power is x²yz

∴ The greatest common factor = 21x²yz

5. 12ax², 6a²x³ and 2a³x⁵

Solution:

We know that the numerical coefficients of given numerical are 12, 6 and 2

Greatest common factor of 12, 6 and 2 is 2.

Common literals appearing in given numerical are a and x

Smallest power of x in three monomials is 2

Smallest power of a in three monomials is 1

Monomials of common literals with smallest power is ax²

∴ The greatest common factor = 2ax²

6. 9x², 15x²y³, 6xy² and 21x²y²

Solution:

We know that the numerical coefficients of given numerical are 9, 15, 16 and 21

Greatest common factor of 9, 15, 16 and 21 is 3.

Common literals appearing in given numerical are x and y

Smallest power of x in four monomials is 1

Smallest power of y in four monomials is 0

Monomials of common literals with smallest power is x

∴ The greatest common factor = 3x

7. 4a²b³, -12a³b, 18a⁴b³

Solution:

We know that the numerical coefficients of given numerical are 4, -12 and 18.

Greatest common factor of 4, -12 and 18 is 2.

Common literals appearing in given numerical are a and b

Smallest power of a in three monomials is 2

Smallest power of b in three monomials is 1

Monomials of common literals with smallest power is a²b

∴ The greatest common factor = 2a²b

8. 6x²y², 9xy³, 3x³y²

Solution:

We know that the numerical coefficients of given numerical are 6, 9 and 3

Greatest common factor of 6, 9 and 3 is 3.

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 1

Smallest power of y in three monomials is 2

Monomials of common literals with smallest power is xy²

∴ The greatest common factor = 3xy²

9. a²b³, a³b²

Solution:

We know that the numerical coefficients of given numerical are 0

Common literals appearing in given numerical are a and b

Smallest power of a in two monomials = 2

Smallest power of b in two monomials = 2

Monomials of common literals with smallest power is a²b²

∴ The greatest common factor = a²b²

10. 36a²b²c⁴, 54a⁵c², 90a⁴b²c²

Solution:

We know that the numerical coefficients of given numerical are 36, 54 and 90

Greatest common factor of 36, 54 and 90 is 18.

Common literals appearing in given numerical are a, b and c

Smallest power of a in three monomials is 2

Smallest power of b in three monomials is 0

Smallest power of c in three monomials is 2

Monomials of common literals with smallest power is a²c²

∴ The greatest common factor = 18a²c²

11. x³, -yx²

Solution:

We know that the numerical coefficients of given numerical are 0

Common literals appearing in given numerical are x and y

Smallest power of x in two monomials is 2

Smallest power of y in two monomials is 0

Monomials of common literals with smallest power is x²

∴ The greatest common factor = x²

12. 15a³, -45a², -150a

Solution:

We know that the numerical coefficients of given numerical are 15, -45 and 150

Greatest common factor of 15, -45 and 150 is 15.

Common literals appearing in given numerical is a

Smallest power of a in three monomials is 1

Monomials of common literals with smallest power is a

∴ The greatest common factor = 15a

13. 2x³y², 10x²y³, 14xy

Solution:

We know that the numerical coefficients of given numerical are 2, 10 and 14.

Greatest common factor of 2, 10 and 14 is 2.

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 1

Smallest power of y in three monomials is 1

Monomials of common literals with smallest power is xy

∴ The greatest common factor = 2xy

14. 14x³y⁵, 10x⁵y³, 2x²y²

Solution:

We know that the numerical coefficients of given numerical are 14, 10 and 2.

Greatest common factor of 14, 10 and 2 is 2.

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 2

Smallest power of y in three monomials is 2

Monomials of common literals with smallest power is x²y²

∴ The greatest common factor = 2x²y²

Find the greatest common factor of the terms in each of the following expressions:

15. 5a⁴ + 10a³ – 15a²

Solution:

The greatest common factor of the three terms is 5a²

16. 2xyz + 3x²y + 4y²

Solution:

The greatest common factor of the three terms is y

17. 3a²b² + 4b²c² + 12a²b²c²

Solution:

The greatest common factor of the three terms is b².