Grade 8 Factorization Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Find the Common Factors of Each Pair of Expressions. Then Find Their Highest Common Factor (HCF)

(a)

(2) Answer these questions from given polynomial .

(a) What is the integer coefficient of the HCF of the three terms?

(b) Which is the only variable common to the three terms?

(3) Answer these questions from given polynomial

(a) What is the integer coefficient of the HCF of the three terms?

(b) What is the power of a in the HCF of the three terms?

(c) What is the power of c in the HCF of the three terms?

(4) Factorize by Taking-Out the HCF

(a)

(b)

(5) Factorize by Taking-Out the HCF

(a)

(b)

(6) Factorize the Expression

(a)

(b)

(c)

(7) Factorize using the identity

(a)

(8) Factorize

(a)

(9) Factorize

(a)

(10) Factorize

(a)

(11) Factorize

(a)

(12) Factorize

(a)

(13) Factorize

(a)

(14) Factorize

(a)

Answers and Explanations

Answer 1 (A)

  • To find out common factor of given polynomial first we factorize the polynomial
  • Factor of ,

  • Now factor of another polynomial,

  • Now from above HCF of given polynomial are as below,

Answer 2 (A)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • Now factor of

  • Now factor of

  • Now from above HCF of given polynomial are as below,

  • Hence Integer coefficient of the HCF of three terms is

Answer 2 (B)

  • HCF of given polynomial is
  • Hence only variable common to the three terms

Answer 3 (A)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • Factor of

  • Factor of

  • Now for HCF of integer coefficient we can easily find it out by its factorize form and for variable (a, b, c) we take least power of variable among all three polynomial
  • For example for variable ā€œaā€ is least power among all three polynomial hence for variable ā€œaā€ we take as a part of HCF.
  • Hence

  • Hence from HCF integer coefficient ofHCF of the three terms is

Answer 3 (B)

  • HCF of given polynomial is
  • Hence power of ā€œaā€ in the HCF of the three terms

Answer 3 (C)

  • HCF of given polynomial is
  • Hence power of ā€œcā€ in the HCF of the three terms

Answer 4 (A)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • And factor of

  • Hence HCF is
  • Now,

Answer 4 (B)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • And factor of

  • Hence HCF is

  • Now,

Answer 5 (A)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • Factor of

  • Hence HCF is

  • Now,

Answer 5 (B)

  • To find HCF of given polynomial first we factorize given polynomial.
  • Factor of

  • Factor of

  • Hence HCF is

  • Now,

Answer 6 (A)

  • Hence ,

Answer 6 (B)

  • Therefore,

Answer 6 (C)

  • Therefore,

Answer 7 (A)

  • Compare this equation with identities
  • Hence ,

  • Now compare with identities
  • Hence

  • Now Compare with identities
  • Hence

  • Hence from Equation 1,2 and 3

Answer 8 (A)

  • Compare this equation with identities
  • Hence

  • Hence

  • Hence,

Answer 9 (A)

  • Given equation,
  • Now Guess
  • Hence our equation is

  • Compare this equation with identities
  • Hence we have,

  • Hence

  • Now put the value of in above equation,

  • Hence,

Answer 10 (A)

  • Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of
  • Hence
  • Multiplication of coefficient
  • Now,
Illustration 2 for Answers_and_Explanations
  • So,

  • Hence,

Answer 11 (A)

  • Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of
  • Hence
  • Multiplication of coefficient
  • Now,
Illustration 3 for Answers_and_Explanations
  • So,

  • Hence,

Answer 12 (A)

  • Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of
  • Hence
  • Multiplication of coefficient
  • Now,
Illustration 4 for Answers_and_Explanations
  • So

  • Hence,

Answer 13 (A)

  • Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of
  • Hence
  • Multiplication of coefficient
  • Now,
Illustration 5 for Answers_and_Explanations
  • So

  • Hence,

Answer 14 (A)

  • Now Assume
  • Hence our equation will be,

  • Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of
  • So, multiplication of coefficient
  • Now,
Illustration 6 for Answers_and_Explanations
  • So

  • Hence,
  • Now , put the value of

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