8th Class Mathematics Factorisation Question Bank

done Factorisation Total Questions - 50

• question_answer1)
  What are the factors of \[ax+by+bx+az+ay+bz\]?
  A)
   \[(bx+ay),(ax+by)\] done clear
  B)
   \[(a+b),(2x+2y+2z)\] done clear
  C)
   \[(x+y+z),(a+b)\] done clear
  D)
   \[(x+y-z),(a-b)\] done clear
  View Solution play_arrow

• question_answer2)
  Which of the following is one of the factors of \[{{x}^{4}}+4\]?
  A)
   \[{{x}^{2}}+2\]                                 done clear
  B)
   \[{{x}^{2}}-2x+2\]           done clear
  C)
           \[{{x}^{2}}-2\]                 done clear
  D)
          \[{{x}^{2}}+2x-2\]                           done clear
  View Solution play_arrow

• question_answer3)
  What are the factors of \[{{x}^{4}}+2{{x}^{2}}+9\]?
  A)
   \[({{x}^{2}}+2x+3),({{x}^{2}}-2x+3)\] done clear
  B)
   \[({{x}^{2}}+3),({{x}^{2}}-3)\] done clear
  C)
   \[({{x}^{2}}+2x+3),({{x}^{2}}+2x+3)\] done clear
  D)
   \[({{x}^{2}}+3),({{x}^{2}}+3)\] done clear
  View Solution play_arrow

• question_answer4)
  For \[{{x}^{2}}+2x+5\]to be a factor of \[{{x}^{4}}+\text{ }p{{x}^{2}}+q,\]what must the respective values of p and q be?
  A)
   \[-2\] and \[5\]                                done clear
  B)
   \[5\] and \[25\] done clear
  C)
   \[10\] and \[20\]    done clear
  D)
   \[6\] and \[25\] done clear
  View Solution play_arrow

• question_answer5)
  What are the factors of \[{{x}^{2}}+xy-2xxz-2yz\]?
  A)
   \[(x-y)\] and \[(x+2z)\] done clear
  B)
   \[(x+y)\] and \[(x-2z)\] done clear
  C)
   \[(x-y)\]and \[(x-2z)\] done clear
  D)
   \[(x+y)\] and \[(x+2z)\] done clear
  View Solution play_arrow

• question_answer6)
  Amrit and Pankaj expanded \[{{(x-5)}^{2}}\]. Amrit's answer is \[{{x}^{2}}-25\] and Pankaj's answer is \[{{x}^{2}}-10x+25\].Which of the following statements is correct?
  A)
   Amrit's answer is correct. done clear
  B)
   Pankaj's answer is wrong. done clear
  C)
   Both got correct answer. done clear
  D)
   Pankaj's answer is correct. done clear
  View Solution play_arrow

• question_answer7)
  Find the quotient when \[5{{a}^{2}}{{b}^{2}}{{c}^{2}}\] is divided by15abc.
  A)
   \[\frac{abc}{3}\]                                              done clear
  B)
   \[3\,abc\]           done clear
  C)
          \[3\,{{a}^{2}}{{b}^{2}}{{c}^{2}}\]              done clear
  D)
          \[5\,{{a}^{2}}{{b}^{2}}{{c}^{2}}\]                              done clear
  View Solution play_arrow

• question_answer8)
  Which of the following statements is correct?
  A)
   \[(a-4)\,(a-2)={{a}^{2}}+8-6a\] done clear
  B)
   \[(2p+3q)\,(p-q)=2{{p}^{2}}-3{{q}^{2}}\] done clear
  C)
   \[\frac{3{{p}^{2}}}{3{{p}^{2}}}=0\] done clear
  D)
   \[4\,(m-5)=4m-5\] done clear
  View Solution play_arrow

• question_answer9)
  What are the factors of\[{{x}^{4}}+{{y}^{4}}+{{x}^{2}}{{y}^{2}}\]?
  A)
   \[({{x}^{2}}+{{y}^{2}})\] and \[({{x}^{2}}+{{y}^{2}}-xy)\] done clear
  B)
   \[({{x}^{2}}+{{y}^{2}})\]and \[({{x}^{2}}-{{y}^{2}})\] done clear
  C)
   \[({{x}^{2}}+{{y}^{2}}+xy)\] and \[({{x}^{2}}+{{y}^{2}}-xy)\] done clear
  D)
   Factorization is not possible. done clear
  View Solution play_arrow

• question_answer10)
  Choose the factors of \[15{{x}^{2}}-26x+8\] from the following.
  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
  View Solution play_arrow

• question_answer11)
  How many factors does \[({{x}^{9}}-x)\] have?
  A)
   \[5\]                                     done clear
  B)
   \[4\]                     done clear
  C)
          \[2\]                     done clear
  D)
          \[9\] done clear
  View Solution play_arrow

• question_answer12)
  Which of the following are the factors of \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}\]?
  A)
   \[\left( \frac{x}{4}+\frac{y}{9} \right)\] and \[\left( \frac{x}{4}-\frac{y}{9} \right)\] done clear
  B)
   \[\left( \frac{x}{2}+\frac{y}{9} \right)\] and \[\left( \frac{x}{2}-\frac{y}{9} \right)\] done clear
  C)
   \[\left( \frac{x}{2}+\frac{y}{3} \right)\]and \[\left( \frac{x}{2}-\frac{y}{3} \right)\] done clear
  D)
   \[\left( \frac{x}{2}-\frac{y}{3} \right)\] and \[\left( \frac{x}{4}-\frac{y}{9} \right)\] done clear
  View Solution play_arrow

• question_answer13)
  What is the coefficient of 'a' when \[9{{a}^{2}}+18a\]is divided by \[(a+2)\]?
  A)
   \[18\]                                   done clear
  B)
   \[9\]                     done clear
  C)
   \[\frac{1}{2}\]                   done clear
  D)
          \[2\]                                     done clear
  View Solution play_arrow

• question_answer14)
                  From the following, which are the factors of \[{{a}^{2}}+b-ab-a\]?                  
  A)
   \[(a-1)\]and \[(a-b)\]              done clear
  B)
   \[(a+b)\]and \[(a-1)\]      done clear
  C)
   \[(a+1)\]and \[(a-b)\]      done clear
  D)
   \[(a+b)\] and \[(a+1)\]                  done clear
  View Solution play_arrow

• question_answer15)
  The expression \[({{p}^{2}}+7p+10)\] is factorized and then divided by \[(p+5)\]. What is the quotient?
  A)
   \[p-5\]                                 done clear
  B)
   \[p-2\] done clear
  C)
          \[p+2\]                done clear
  D)
          \[p+5\]                                done clear
  View Solution play_arrow

• question_answer16)
  Which is the correct statement in the following?
  A)
   \[{{(3m+4)}^{2}}=3{{m}^{2}}+6m+16\] done clear
  B)
   \[n(3n+2)=3{{n}^{2}}+2n\] done clear
  C)
   \[(x-2)\,(x-8)={{x}^{2}}-16\] done clear
  D)
   \[(p+2)\,(p+4)={{p}^{2}}+8\] done clear
  View Solution play_arrow

• question_answer17)
  If \[({{x}^{2}}+3x+5)\,\,({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}},\]what is the value of m?
  A)
   \[{{x}^{2}}-3x\]                                done clear
  B)
   \[3x\]                   done clear
  C)
   \[{{x}^{2}}+5\] done clear
  D)
          \[{{x}^{2}}+3x\] done clear
  View Solution play_arrow

• question_answer18)
  Divide \[6{{p}^{5}}+18{{p}^{4}}-3{{p}^{2}}\] by \[3{{p}^{2}}\].
  A)
   \[6{{p}^{3}}-6{{p}^{2}}+1\] done clear
  B)
   \[2{{p}^{3}}-6{{p}^{2}}-1\] done clear
  C)
   \[2{{p}^{3}}+6{{p}^{2}}-1\] done clear
  D)
   \[2{{p}^{3}}+6{{p}^{2}}+1\] done clear
  View Solution play_arrow

• question_answer19)
  Find the factors of \[{{b}^{2}}-7b+12\].
  A)
   \[(b-4),\,(b-8)\] done clear
  B)
   \[(b-3),\,(b-4)\] done clear
  C)
   \[(b-10),\,(b-1)\] done clear
  D)
   \[(b-7),\,(b-9)\] done clear
  View Solution play_arrow

• question_answer20)
  Find the factors of\[6\text{ }mn-4n+6-9m\].  
  A)
   \[(2m-1)\] and \[(2n-4)\] done clear
  B)
   \[(4m-1)\] and \[(n-3)\] done clear
  C)
   \[(3m-2)\] and \[(2n-3)\] done clear
  D)
   \[(4m-4)\] and \[(n-1)\]             done clear
  View Solution play_arrow

• question_answer21)
  Which of the following is the exponential form of factors of \[{{a}^{2}}+4a+4\]?        
  A)
   \[{{(a+2)}^{2}}\]                              done clear
  B)
   \[{{(a+1)}^{2}}\]              done clear
  C)
          \[{{(a-2)}^{2}}\]               done clear
  D)
          \[{{(a-1)}^{2}}\]                                                               done clear
  View Solution play_arrow

• question_answer22)
  What is the result when \[{{x}^{3}}+6{{x}^{2}}+9x\]is factorized?
  A)
   \[{{x}^{2}}{{(x+2)}^{2}}\]                             done clear
  B)
   \[x{{(x+3)}^{2}}\]            done clear
  C)
          \[x(x+3)\]           done clear
  D)
          \[{{x}^{2}}(x+3)\] done clear
  View Solution play_arrow

• question_answer23)
  What are the factors of \[{{(2x+3y)}^{2}}+2(2x+3y)\,(x+y)+{{(x+y)}^{2}}\]?
  A)
   \[(3x+4y)\] and \[(3x-4y)\] done clear
  B)
   \[(3x+4y)\]and \[(3x+4y)\] done clear
  C)
   \[(3x+2y)\] and \[(2x-3y)\] done clear
  D)
   \[(3x-4y)\] and \[(3x+2y)\] done clear
  View Solution play_arrow

• question_answer24)
  What are the factors of \[{{a}^{2}}{{b}^{2}}+{{c}^{2}}{{d}^{2}}-{{a}^{2}}{{c}^{2}}-{{b}^{2}}{{d}^{2}}\]?
  A)
   \[(a+d),\,(a-d),(b+c)\] and \[(b-c)\] done clear
  B)
   \[({{a}^{2}}-{{b}^{2}})\] done clear
  C)
   \[({{a}^{2}}-{{d}^{2}})\] and \[({{b}^{2}}+{{c}^{2}})\] done clear
  D)
   \[({{a}^{2}}+{{d}^{2}})\] and \[({{b}^{2}}-{{c}^{2}})\] done clear
  View Solution play_arrow

• question_answer25)
  Divide  \[-15{{a}^{2}}b{{c}^{3}}\] by \[-5ab{{c}^{2}}\].
  A)
   \[3{{a}^{1}}c\]                                  done clear
  B)
   \[3{{a}^{2}}c\]  done clear
  C)
   \[3{{a}^{3}}c\]  done clear
  D)
          \[4{{a}^{2}}c\] done clear
  View Solution play_arrow

• question_answer26)
  Simplify \[\frac{-3{{a}^{2}}b\times 15ca{{b}^{2}}}{-10\,cab}\].
  A)
   \[\frac{3}{2}{{a}^{2}}{{b}^{2}}\]                                done clear
  B)
   \[\frac{9}{2}{{a}^{2}}{{b}^{2}}\]                done clear
  C)
   \[\frac{3}{2}{{a}^{3}}{{b}^{3}}\]                done clear
  D)
          \[\frac{7}{2}{{a}^{2}}{{b}^{2}}\] done clear
  View Solution play_arrow

• question_answer27)
  Find the quotient of the algebraic terms in \[\frac{36{{x}^{3}}{{y}^{2}}z}{-9{{x}^{2}}\,{{y}^{2}}z}\].
  A)
   \[4x\]                                   done clear
  B)
   \[4x{{y}^{2}}z\]                done clear
  C)
          \[-4x\]                 done clear
  D)
          \[4{{x}^{3}}{{y}^{2}}z\] done clear
  View Solution play_arrow

• question_answer28)
  Divide: \[4{{p}^{5}}-14{{p}^{4}}+6{{p}^{3}}-2{{p}^{2}}\] by \[2{{p}^{2}}\].
  A)
   \[2{{p}^{3}}+7{{p}^{2}}+3p+1\] done clear
  B)
   \[2{{p}^{3}}-7{{p}^{2}}+3p-1\] done clear
  C)
   \[2{{p}^{3}}-7{{p}^{2}}-3p-1\] done clear
  D)
   \[2{{p}^{3}}+7{{p}^{2}}-3p-1\] done clear
  View Solution play_arrow

• question_answer29)
  Simplify \[\frac{3(4+2{{m}^{2}}-m)-6(3{{m}^{2}}+m+2)}{2(2m-3)+3(m+2)}\]
  A)
                   \[\frac{3(3m+4)}{7}\]    done clear
  B)
                   \[\frac{3(4m+3)}{7}\] done clear
  C)
                   \[3\left( \frac{3m-4}{7} \right)\] done clear
  D)
                   \[\frac{-3(4m+3)}{7}\]       done clear
  View Solution play_arrow

• question_answer30)
  What is the factorization of \[3xz-4yz-6xp+8yp\]?
  A)
   \[(3x+4y)\,(z+2p)\] done clear
  B)
   \[(3x+4y)\,(z-2p)\] done clear
  C)
   \[(3x-4y)\,(z+2p)\] done clear
  D)
   \[(3x-4y)\,(z-2p)\] done clear
  View Solution play_arrow

• question_answer31)
  Give the factor form of \[3(2p-q+4r)+2p+15q-16r\]
  A)
   \[4\,(2p+3q+r)\] done clear
  B)
   \[4\,(2p+3q-r)\] done clear
  C)
   \[4\,(2p-3q+r)\] done clear
  D)
   \[4\,(2p-3q-r)\] done clear
  View Solution play_arrow

• question_answer32)
  Simplify \[\frac{3lm}{8{{n}^{2}}}\times \frac{32{{\ln }^{3}}}{{{m}^{2}}}\div \frac{9{{\ln }^{2}}}{m}\].
  A)
   \[\frac{4l}{3n}\]                                               done clear
  B)
   \[-\frac{4l}{3n}\]             done clear
  C)
          \[\frac{4n}{3l}\]                               done clear
  D)
          \[\frac{-4n}{3l}\]                             done clear
  View Solution play_arrow

• question_answer33)
  Divide \[q(5{{q}^{2}}-80)\] by \[5q(q+4)\].
  A)
   \[5q(q-16)\]                      done clear
  B)
   \[(q-4)\]              done clear
  C)
          \[5q({{q}^{2}}+16)\]      done clear
  D)
          \[(q+16)\] done clear
  View Solution play_arrow

• question_answer34)
  Give the factor form of \[6{{m}^{2}}n+9m{{n}^{2}}l+12mnl\].
  A)
   \[3mn(2m+3nl+4l)\] done clear
  B)
   \[4mn(4m+4nl+2l)\] done clear
  C)
   \[5mn(2m+2nl+l)\] done clear
  D)
   \[3mn(m+2nl+2l)\] done clear
  View Solution play_arrow

• question_answer35)
  Divide \[44({{m}^{4}}-5{{m}^{3}}-24{{m}^{2}})\] by \[11m(m-8)\].
  A)
   \[4{{m}^{2}}(m-3)\] done clear
  B)
   \[4m(m-3)\] done clear
  C)
   \[4{{m}^{2}}(m+3)\] done clear
  D)
   \[4m(m+3)\] done clear
  View Solution play_arrow

• question_answer36)
  Factorize\[49{{x}^{2}}-36\].
  A)
   \[(7x-6)\,(7x+6)\] done clear
  B)
   \[(7x+36)7\] done clear
  C)
   \[(7x+6)6\] done clear
  D)
   \[(7x+6)\,(7x+36)\] done clear
  View Solution play_arrow

• question_answer37)
  Find the factors of \[3{{z}^{2}}+9z+6\].
  A)
   \[3(z+1)\,(z+2)\] done clear
  B)
   \[4(z+2)(z+3)\] done clear
  C)
   \[2(z+3)\,(z+1)\] done clear
  D)
   \[3(z+5)\,(z+5)\] done clear
  View Solution play_arrow

• question_answer38)
  The area of a square is\[({{x}^{2}}+8x+16)c{{m}^{2}}\]. Find the length of its side.
  A)
   \[(x-8)\,cm\]                                     done clear
  B)
   \[(x-4)\,cm\]     done clear
  C)
          \[(x+4)\,cm\]                    done clear
  D)
          \[(x+2)\,cm\]                                                    done clear
  View Solution play_arrow

• question_answer39)
  Which of the following is the correct factorization?
  A)
   \[64-{{x}^{2}}=(64-x)\,(64+x)\] done clear
  B)
   \[27{{x}^{2}}-48=3(3x+4)\,(3x-4)\] done clear
  C)
   \[{{y}^{2}}-81=(y+9)\,(y+9)\] done clear
  D)
   \[36-{{p}^{2}}=(p-6)\,(p+6)\] done clear
  View Solution play_arrow

• question_answer40)
  Which of the following factorizations is incorrect?
  A)
   \[200{{y}^{2}}-2=2(10y+1)\,(10y-1)\] done clear
  B)
   \[49{{x}^{2}}-36=(7x+6)\,(7x-6)\] done clear
  C)
   \[200{{y}^{2}}-2=2(10y+1)\,(10y+1)\] done clear
  D)
   \[36-100{{k}^{2}}=(6+10k)\,(6-10k)\] done clear
  View Solution play_arrow

• question_answer41)
  Choose the factors of \[{{x}^{4}}-13{{x}^{2}}{{y}^{2}}+36{{y}^{4}}\] from the following.
  A)
   \[(x+4y),(x-4y),(x+2y)\]and \[(x-2y)\] done clear
  B)
   \[({{x}^{2}}+2x-8)\] and \[({{x}^{2}}+2x-3)\] done clear
  C)
   \[(x+3y),(x-3y),(x+2y)\]and \[(x-2y)\] done clear
  D)
   \[({{x}^{2}}-2x-8)\] and \[({{x}^{2}}+2x+3)\] done clear
  View Solution play_arrow

• question_answer42)
  What is the factor form of \[9{{x}^{4}}-40{{x}^{2}}+16\]?
  A)
   \[(x+1)\,(x-1)\,(2x+1)\,(2x-1)\] done clear
  B)
   \[(2x-1)\,(4{{x}^{2}}+2x+1)\] done clear
  C)
   \[(x+2)\,(2x-3)(x-1)\,(2x+3)\] done clear
  D)
   \[(x+2)\,(x-2)\,(3x+2)\,(3x-2)\] done clear
  View Solution play_arrow

• question_answer43)
  What is the perfect square form of \[9{{a}^{2}}-\frac{12}{5}a+\frac{4}{25}\]?
  A)
   \[{{\left( a-\frac{2}{5} \right)}^{2}}\]      done clear
  B)
   \[{{\left( 3a-\frac{2}{5} \right)}^{2}}\]    done clear
  C)
   \[{{\left( 2a-\frac{2}{5} \right)}^{2}}\]    done clear
  D)
          \[{{\left( 3a+\frac{2}{5} \right)}^{2}}\]                   done clear
  View Solution play_arrow

• question_answer44)
  Choose the factors of \[a{{(x-y)}^{2}}-by+bx+3x-3y.\]
  A)
   \[(x-y)\] and \[\left[ a(x-y)+b+3 \right]\] done clear
  B)
   \[(a-b)\] and \[(3x-3y)\] done clear
  C)
   \[(x-y)\] and \[({{x}^{2}}+a+1)\] and \[({{y}^{2}}+b+1)\] done clear
  D)
   \[(ax-y)\] and \[[a(x-y)+b+3]\] done clear
  View Solution play_arrow

• question_answer45)
  Find the factors of \[{{x}^{2}}+\frac{{{a}^{2}}-1}{a}x-1\]from the following.
  A)
   \[\left( x-\frac{1}{a} \right)\] and \[(x+a)\] done clear
  B)
   \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\] done clear
  C)
   \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x-a)\] done clear
  D)
   \[\left( x+\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\] done clear
  View Solution play_arrow

• question_answer46)
  What is the factor form of \[{{\left( {{p}^{2}}+{{q}^{2}}-{{r}^{2}} \right)}^{2}}-4{{p}^{2}}{{q}^{2}}\]?
  A)
   \[(p+q+r)\,(p+q-r)\]\[(p-q+r)\,(p-q-r)\] done clear
  B)
   \[(p-q-r)\,({{p}^{2}}-{{q}^{2}}-{{r}^{2}})\] done clear
  C)
   \[(p-q-r)\] \[(2p-2q-2r)\] done clear
  D)
   \[(p+q-r)\,({{p}^{2}}-{{q}^{2}}-{{r}^{2}})\] done clear
  View Solution play_arrow

• question_answer47)
  What is the quotient when \[12ab\,{{(9{{a}^{2}}-16b)}^{2}}\] is divided by \[4ab\,(3a+4b)\]?
  A)
           \[4\,(3a+4b)\]  done clear
  B)
          \[3\,(3a-4b)\]                   done clear
  C)
                   \[3\,(3a+4b)\]  done clear
  D)
          \[4\,(3a-4b)\] done clear
  View Solution play_arrow

• question_answer48)
  Identify the factors of\[18-32{{p}^{2}}\].
  A)
   \[2(4p+3)\,(4p-3)\] done clear
  B)
   \[2(3+4p)\,(3-4p)\] done clear
  C)
   \[4(3+4p)\,(3-4p)\] done clear
  D)
   \[4(3+2p)\,(3-2p)\] done clear
  View Solution play_arrow

• question_answer49)
  Which of the following factorizations is incorrect?
  A)
   \[27k-5{{k}^{2}}=k(27-5k)\] done clear
  B)
   \[6{{y}^{2}}-12y=6y(y-2)\] done clear
  C)
   \[16x-4{{x}^{2}}=4x(4-{{x}^{2}})\] done clear
  D)
   \[121{{n}^{2}}-22n=11n(11n-2)\] done clear
  View Solution play_arrow

• question_answer50)
  Which of the following factorizations is correct?
  A)
   \[2-32{{x}^{2}}=2{{(1-4x)}^{2}}\] done clear
  B)
   \[4{{x}^{2}}-49=(7-2x)\,(7+2x)\] done clear
  C)
   \[-18{{x}^{2}}+27x=9x(2x-3)\] done clear
  D)
   \[-25-150{{p}^{2}}=(-25)\,(1+6{{p}^{2}})\] done clear
  View Solution play_arrow