8th Class Mathematics Factorisation Question Bank

done Factorisation Total Questions - 20

• question_answer1)
  Factorisation of \[xy-pq+qy-px\]is ______.
  A)
   \[(y-p)(x+q)\]  done clear
  B)
   \[(y-p)(x-q)\] done clear
  C)
          \[(y+p)(x+q)\] done clear
  D)
          \[(y+p)(x-q)\]  done clear
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• question_answer2)
  If \[({{x}^{2}}+3x+5)({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}}\]then m=_____.
  A)
   \[{{x}^{2}}-3x\]                  done clear
  B)
   \[3x\]   done clear
  C)
   \[{{x}^{2}}+5\]                  done clear
  D)
   Both (a) and (b) done clear
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• question_answer3)
  The factors of \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}\]are ____.
  A)
   \[\left( \frac{x}{4}+\frac{y}{9} \right)\left( \frac{x}{4}-\frac{y}{9} \right)\] done clear
  B)
   \[\left( \frac{x}{2}+\frac{y}{9} \right)\left( \frac{x}{2}-\frac{y}{9} \right)\] done clear
  C)
   \[\left( \frac{x}{2}+\frac{y}{3} \right)\left( \frac{x}{2}-\frac{y}{3} \right)\] done clear
  D)
   Both (a) and (b) done clear
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• question_answer4)
  The factors of \[15{{x}^{2}}-26x+8\]are __.
  A)
   \[(3x-4)(5x+2)\]          done clear
  B)
   \[(3x-4)(5x-2)\]            done clear
  C)
   \[(3x+4)(5x-2)\]          done clear
  D)
   \[(3x+4)(5x+2)\]        done clear
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• question_answer5)
  The factors of \[{{x}^{2}}-16\] are __.
  A)
   \[({{x}^{2}}+2)({{x}^{2}}-2)\] done clear
  B)
   \[(x+4)(x-4)\] done clear
  C)
   \[(x+2)(x-2)\] done clear
  D)
   Does not exist done clear
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• question_answer6)
  The factors of \[\sqrt{3}{{x}^{2}}+11x+6\sqrt{3}\] are __.
  A)
   \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] done clear
  B)
   \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\] done clear
  C)
   \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\] done clear
  D)
   \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] done clear
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• question_answer7)
  Factors of \[{{x}^{4}}-{{(x-z)}^{4}}\] are __.
  A)
   \[(2x+z)(2{{x}^{3}}+{{z}^{3}}-2{{x}^{2}})\] done clear
  B)
   \[z(x+2z)({{x}^{2}}+{{z}^{2}}-{{x}^{2}})\] done clear
  C)
   \[z(2x-z)(2{{x}^{2}}-2xz+{{z}^{2}})\] done clear
  D)
   \[z(x-2z)(2{{z}^{2}}-2xz+{{x}^{2}})\] done clear
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• question_answer8)
  Factorising \[{{(x-y)}^{2}}+4xy-{{z}^{2}}\], we get
  A)
   \[(x+y+z)(x+y-z)\] done clear
  B)
   \[(y-y-z)(x+y-z)\] done clear
  C)
   \[(x-y+z)(x+y-z)\] done clear
  D)
   None of these done clear
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• question_answer9)
  The factors of \[{{x}^{4}}+{{y}^{4}}+{{x}^{2}}{{y}^{2}}\] are _____.
  A)
   \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-xy)\] done clear
  B)
   \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}-{{y}^{2}})\] done clear
  C)
   \[({{x}^{2}}+{{y}^{2}}+xy)({{x}^{2}}+{{y}^{2}}-xy)\] done clear
  D)
   Factorisation is not possible done clear
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• question_answer10)
  For \[{{x}^{2}}+2x+5\] to be a factor of\[x4+p{{x}^{2}}+q\], the values of p and q must be _____.
  A)
   -2, 5                done clear
  B)
   5, 25   done clear
  C)
   10, 20             done clear
  D)
   6, 25   done clear
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• question_answer11)
  One of the factors of \[4(x+y)\,(3a-b)+6(x+y)\,(2b-3a)\] is
  A)
   \[(2b-3a)\]                   done clear
  B)
   \[(3a-b)\]         done clear
  C)
   \[(4a-3b)\]                   done clear
  D)
   \[(-3a+4b)\]    done clear
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• question_answer12)
  Divide \[(32{{x}^{4}}{{y}^{3}}-16{{x}^{3}}{{y}^{4}})\] by \[(-8{{x}^{2}}y)\]
  A)
  \[4{{x}^{3}}{{y}^{2}}+2x{{y}^{3}}\]            done clear
  B)
   \[4{{x}^{3}}y-2x{{y}^{3}}\]       done clear
  C)
   \[-4{{x}^{2}}{{y}^{2}}+2x{{y}^{3}}\] done clear
  D)
          \[-4x{{y}^{2}}+2x{{y}^{3}}\]    done clear
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• question_answer13)
  One of the factors of (\[{{(p+q)}^{2}}-{{(a-b)}^{2}}\]\[+p+q-a+b\] is
  A)
   \[(p+q+a+b)\]          done clear
  B)
   \[(p+q-a+b)\] done clear
  C)
   \[(p-q+a-b)\] done clear
  D)
          \[(p-q+a+b)\] done clear
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• question_answer14)
  Factorise\[{{(2x+3y)}^{2}}-5(2x+3y)\]- 14.
  A)
  \[4(2x+3y)(x+y-2)\] done clear
  B)
   \[4(2x+3y)(x+y+2)\] done clear
  C)
   \[(2x-3y+7)(2x-3y+2)\] done clear
  D)
   \[(2x+3y-7)(2x+3y+2)\] done clear
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• question_answer15)
  Simplify:- \[\frac{-14{{x}^{12}}y+8{{x}^{5}}z}{2{{x}^{2}}}\]
  A)
  \[{{x}^{3}}(-7{{x}^{7}}y+4z)\]  done clear
  B)
   \[{{x}^{2}}(7{{x}^{7}}y-4z)\]     done clear
  C)
   \[{{x}^{2}}(-7{{x}^{6}}y+2z)\] done clear
  D)
   \[{{x}^{3}}(-7{{x}^{7}}y+4z)\] done clear
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• question_answer16)
  Which of the following is the factor of \[12{{({{a}^{2}}+7a)}^{2}}-8({{a}^{2}}+7a)(2a-1)-15{{(2a-1)}^{2}}\]?

  (i) \[(2{{a}^{2}}+8a+3)\]

  (ii) \[(6{{a}^{2}}+52a-5)\]

  (iii) \[\text{(3a+5)}\]

  A)
   Only (i)                       done clear
  B)
   Both (i) and (ii)           done clear
  C)
   Only (ii)                      done clear
  D)
   All (i), (ii) and (iii)       done clear
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• question_answer17)
  Fill in the blanks.

  (i) \[\frac{{{a}^{2}}-{{b}^{2}}}{a(a-b)}-\frac{a{{b}^{2}}+{{a}^{2}}b}{a{{b}^{2}}}\] is equal to    P   .

  (ii) \[\frac{64{{y}^{4}}+8{{y}^{3}}}{4{{y}^{3}}}\] is equal to     Q    .

  (iii) When we divide \[(38{{a}^{3}}{{b}^{3}}{{c}^{2}}-19{{a}^{4}}{{b}^{2}}c)\] by \[19{{a}^{2}}bc\], the result is \[ka{{b}^{2}}c-{{a}^{2}}b\]. Then \[k=\underline{\,\,\,R\,\,\,}\].

  A)

  P	Q	R
  \[\frac{(a+b)(b-a)}{ab}\]	\[3(8y+1)\]	1

                  done clear
  B)

  P	Q	R
  \[\frac{(a+b\,)(b-a)}{ab}\]	\[3(8y+1)\]	1

                  done clear
  C)

  P	Q	R
  \[\frac{(a+b)(a-b)}{ab}\]	\[2(8y+1)\]	1

                  done clear
  D)

  P	Q	R
  \[\frac{(a+b)(b-a)}{ab}\]	\[2(8y+1)\]	2

  done clear
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• question_answer18)
  Which of the following statements is CORRECT?
  A)
   The factors of an expression are always either algebraic variable or algebraic expression. done clear
  B)
   An irreducible factor is a factor that cannot be expressed further as a product of factors. done clear
  C)
   Every binomial expression can be factorised into two monomial expression. done clear
  D)
   The process of writing a given expression as the product of two or more factors is called multiplication of factors. done clear
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• question_answer19)
  Match the expression given in Column-I to one of their factors given in Column-II.

  Column - I	Column - II
  P. \[9{{x}^{2}}+24x+16\]	(i) \[(2x-4)\]
  Q. \[25{{x}^{2}}+30x+9\]	(ii) \[(4x+1)\]
  R. \[40{{x}^{2}}+14x+1\]	(iii) \[(5x+3)\]
  S. \[4{{x}^{2}}-16x+16\]	(iv) \[(3x+4)\]

  A)
   P\[\to \](iv); Q\[\to \](iii); R\[\to \](ii); S\[\to \](i) done clear
  B)
   P\[\to \](iii): Q\[\to \](i); R\[\to \](iv); S\[\to \](ii) done clear
  C)
   P\[\to \](ii); Q\[\to \](i); R\[\to \](iv): S\[\to \](iii) done clear
  D)
   P\[\to \](iv); Q\[\to \](iii); R\[\to \](i); S\[\to \](ii) done clear
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• question_answer20)
  Do as directed.

  (i) Factorise: \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-3\]

  (ii) Find the greatest common factors of \[14{{x}^{2}}{{y}^{3}},21{{x}^{3}}{{y}^{2}}\] and \[35{{x}^{4}}{{y}^{5}}z\].

  (iii) Divide \[z(5{{z}^{2}}-80)\]by \[5z(z+4)\].

  A)

  (i)	(ii)	(iii)
  \[\left( x-\frac{1}{x} \right)\left( x-\frac{1}{x}-2 \right)\]	\[7x{{y}^{2}}\]	\[z-4\]

                  done clear
  B)

  (i)	(ii)	(iii)
  \[\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x}+2 \right)\]	\[7{{x}^{2}}y\]	\[z-4\]

                  done clear
  C)

  (i)	(ii)	(iii)
  \[\left( x-\frac{1}{x}+1 \right)\left( x-\frac{1}{x}-1 \right)\]	\[7{{x}^{2}}{{y}^{2}}\]	\[z-4\]

                  done clear
  D)

  (i)	(ii)	(iii)
  \[\left( x-\frac{1}{x}-1 \right)\left( x+\frac{1}{x}+1 \right)\]	\[7{{x}^{2}}{{y}^{2}}\]	\[z-2\]

  done clear
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