8th Class Mental Ability Factorisation Question Bank

done Factorisation Total Questions - 40

• question_answer1)
  Identify the factors of \[12ax+3ay+8bx+2by.\]
  A)
  \[~\left( 2a+3b \right)\] and \[(x+2y)\]         done clear
  B)
  \[(2a+b)\] and\[(4x+3y)\] done clear
  C)
  \[(4a+b)\]and\[~\left( x+3y \right)\] done clear
  D)
            \[(3a+2b)\]and \[(4x+y)\] done clear
  View Solution play_arrow

• question_answer2)
  Find the quotient obtained when \[15{{x}^{2}}-26x+8\]is divided by \[5x-2.\]
  A)
  \[6x-1\]                done clear
  B)
         \[~2x+3\]            done clear
  C)
         \[~4x+5\]            done clear
  D)
         \[3x-4\]                                done clear
  View Solution play_arrow

• question_answer3)
  One of the factors of \[2x-32{{x}^{5}}\]is P. Find P.
  A)
  \[~32x\]               done clear
  B)
         \[1+4{{x}^{2}}\]                done clear
  C)
         \[~1-8x\]      done clear
  D)
                         \[1+2{{x}^{2}}\]                                done clear
  View Solution play_arrow

• question_answer4)
  Identify the quotient of \[{{(a-1)}^{2}}-{{(a-2)}^{2}}\div (2a-3).\]
  A)
  0              done clear
  B)
         3              done clear
  C)
         1              done clear
  D)
         -2                                            done clear
  View Solution play_arrow

• question_answer5)
  Which of the following trinomials has \[(y-3)\] as one of its factors?
  A)
  \[{{y}^{2}}-4y-12\]           done clear
  B)
         \[{{y}^{2}}-7y+12\]          done clear
  C)
  \[6{{y}^{2}}-y-2\]             done clear
  D)
         \[3{{y}^{2}}+5y-12\] done clear
  View Solution play_arrow

• question_answer6)
  Which two binomials when multiplied give \[5ct-5c+6-6t?\]
  A)
  \[(5c-6)\]and \[(t-1)\]    done clear
  B)
  \[(5c+6)\]and \[(t+1)\] done clear
  C)
         \[(6c+1)\]and \[(t+5)\]  done clear
  D)
  \[(6c-1)\]and \[(t-5)\]    done clear
  View Solution play_arrow

• question_answer7)
  Find the common factor of the terms\[3{{x}^{2}}yz,24x{{y}^{2}}z\]and \[15xy{{z}^{2}}.\]
  A)
  \[~3{{x}^{2}}{{y}^{2}}{{z}^{2}}\]                done clear
  B)
         \[~3xyz\]        done clear
  C)
  \[3{{x}^{3}}{{y}^{3}}{{z}^{3}}\]                   done clear
  D)
         \[6{{x}^{2}}{{y}^{2}}{{z}^{2}}\]   done clear
  View Solution play_arrow

• question_answer8)
  A rectangular garden has an area of\[~3{{x}^{2}}-11x+6\] square units. Find the measure of one of its sides.
  A)
  \[x+6\]                 done clear
  B)
         \[3x+2\]               done clear
  C)
         \[x+4\]                 done clear
  D)
         \[x3\]    done clear
  View Solution play_arrow

• question_answer9)
  Which value of ?m? would make \[18+mx-{{x}^{2}}\]factorable?
  A)
  8              done clear
  B)
         -2            done clear
  C)
         -7 done clear
  D)
         -1        done clear
  View Solution play_arrow

• question_answer10)
  The area of a square is \[4{{a}^{2}}-12ab+9{{b}^{2}}\]square units. Which of the given expressions represents a side of the square?
  A)
  (4a + 9b) units    done clear
  B)
             (4a - 9b) units done clear
  C)
         (2a + 3b) units     done clear
  D)
             (2a - 3b) units           done clear
  View Solution play_arrow

• question_answer11)
  \[{{(2x+3y)}^{2}}+2(2x+3y)(x+y)+{{(x+y)}^{2}}\]is resolved into two binomial factors. Find them.
  A)
  \[(2x+3y)\]and \[(2x+3y)\] done clear
  B)
         \[(x+y)\]and \[(3x+2y)\] done clear
  C)
  \[(3x+4y)\]and \[(3x+4y)\] done clear
  D)
  \[(4x+y)\]and \[(x+2y)\] done clear
  View Solution play_arrow

• question_answer12)
  If\[a\,\text{+}b=11\]and \[ab=30,\]find the value of a - b.           
  A)
  ± 1         done clear
  B)
  ± 2          done clear
  C)
         ± 4          done clear
  D)
  ± 3                                          done clear
  View Solution play_arrow

• question_answer13)
  Which of these expressions does not have x +\[x+3\] as one of its factors?
  A)
  \[{{x}^{2}}+7x+12\]         done clear
  B)
         \[{{x}^{2}}+x-12\]            done clear
  C)
         \[{{x}^{2}}-x-12\]             done clear
  D)
         \[{{x}^{2}}-2x-15\] done clear
  View Solution play_arrow

• question_answer14)
  Find the factors of \[25{{x}^{2}}-60xy+36{{y}^{2}}.\]
  A)
  \[(5x-3y)\]and\[(5x-12y)\] done clear
  B)
         \[(6x-5y)\]and\[(6x-2y)\] done clear
  C)
  \[(5x-4y)\]and\[(5x-9y)\] done clear
  D)
          \[(5x-3y)\]and\[(5x-3y)\] done clear
  View Solution play_arrow

• question_answer15)
  Which of the following trinomials has the binomial \[2x-3y\] as one of its factors?
  A)
  \[4{{x}^{2}}+12xy-9{{y}^{2}}\] done clear
  B)
  \[4{{x}^{2}}-12xy-9{{y}^{2}}\] done clear
  C)
  \[-4{{x}^{2}}-12xy+9{{y}^{2}}\] done clear
  D)
  \[4{{x}^{2}}-12xy+9{{y}^{2}}\] done clear
  View Solution play_arrow

• question_answer16)
  Identify the factors of \[16-81{{a}^{4}}.\]
  A)
  \[(4+9{{a}^{2}}),(2+3a)\]and \[(2-3a)\] done clear
  B)
  \[(4-9{{a}^{2}}),(2-3a)\]and \[(2-3a)\] done clear
  C)
  \[(4-9{{a}^{2}}),(2a-3)\]and \[(2+3a)\] done clear
  D)
  \[(4-9{{a}^{2}}),(2+3a)\]and \[(2-3a)\] done clear
  View Solution play_arrow

• question_answer17)
  Find the binomials obtained when\[{{(3x+2y)}^{2}}-2(3x+2y)(x+y)\]\[+\,{{(x+y)}^{2}}\]is  resolved into factors.
  A)
  \[(3x+y)\]and \[(3x+y)\] done clear
  B)
  \[(2x+y)\]and \[(2x+y)\] done clear
  C)
  \[(5x+y)\]and \[(5x+y)\] done clear
  D)
  \[(5x+4y)\]and \[(5x+4y)\] done clear
  View Solution play_arrow

• question_answer18)
  If \[\frac{{{y}^{2}}-1}{y+1}=4,\]find the value of y.
  A)
  1                                              done clear
  B)
  1                              done clear
  C)
  5                              done clear
  D)
         3                              done clear
  View Solution play_arrow

• question_answer19)
  What is the value of \[\frac{{{(2013+2012)}^{2}}+{{(2013-2012)}^{2}}}{2013\times 2013+2012\times 2012}?\]
  A)
  6                              done clear
  B)
         4                              done clear
  C)
  2                              done clear
  D)
         3                                              done clear
  View Solution play_arrow

• question_answer20)
  Find the continued product \[(a+2)(a-2)({{a}^{2}}+4).\]
  A)
  \[{{a}^{2}}-16\] done clear
  B)
         \[{{a}^{4}}+16\]                done clear
  C)
         \[{{a}^{2}}+16\]                done clear
  D)
         \[{{a}^{4}}-16\] done clear
  View Solution play_arrow

• question_answer21)
  What are the possible expressions for the dimensions of the cuboid whose volume is \[2{{x}^{2}}+10x+12?\]
  A)
  Length = 2, breadth\[=x+3,\] height \[=x+2\] done clear
  B)
  Length = 5, breadth \[=x+4,\]height\[=x+3\] done clear
  C)
  Length = 3, breadth \[=x+6,\]height \[=x+2\] done clear
  D)
  Length\[=4,\]breadth\[=x-12,\]height \[=x-1\] done clear
  View Solution play_arrow

• question_answer22)
  If one of the factors of \[12-4x-5{{x}^{2}}\]is \[x+2,\]find the other.
  A)
  \[5x+6\]                               done clear
  B)
  \[5x-6\]                done clear
  C)
  \[6-5x\]                done clear
  D)
         \[-5x-6\]                                              done clear
  View Solution play_arrow

• question_answer23)
  The factors of \[{{a}^{2}}{{b}^{2}}+{{c}^{2}}{{d}^{2}}-{{a}^{2}}{{c}^{2}}-{{b}^{2}}{{d}^{2}}\]are binomials A and B. Identify them.
  A)
  \[A=({{b}^{2}}-{{c}^{2}})\] and \[B=({{a}^{2}}+{{d}^{2}})\] done clear
  B)
  \[A=({{b}^{2}}-{{c}^{2}})\]and \[B=({{a}^{2}}-{{d}^{2}})\] done clear
  C)
  \[A=({{a}^{2}}-{{b}^{2}})\]and \[B=({{c}^{2}}-{{d}^{2}})\] done clear
  D)
  \[A=({{a}^{2}}-{{c}^{2}})\]and \[B=({{b}^{2}}-{{d}^{2}})\] done clear
  View Solution play_arrow

• question_answer24)
  If \[x-y=3\]and \[{{x}^{2}}+{{y}^{2}}=29,\]find the value of \[xy:\]
  A)
  11                                           done clear
  B)
  10                           done clear
  C)
  12                           done clear
  D)
         13 done clear
  View Solution play_arrow

• question_answer25)
  The product of two binomials is \[25{{(m+n)}^{2}}-36{{(m-2n)}^{2}}.\]Find them.
  A)
  (5m - n) and (6m -n)         done clear
  B)
  (m + 5n) and (m - 6n) done clear
  C)
  (5n - m) and (6n - m)         done clear
  D)
  (11m - 7n) and (17n - m) done clear
  View Solution play_arrow

• question_answer26)
  Find the factors of\[~8{{x}^{6}}-65{{x}^{3}}+8.\]
  A)
  \[(8{{x}^{2}}-1)\] and \[({{x}^{2}}-8)\]          done clear
  B)
  \[(2{{x}^{3}}-1)\]and \[({{x}^{3}}-8)\] done clear
  C)
  \[(8{{x}^{3}}-1)\]and\[({{x}^{3}}-8)\]          done clear
  D)
  \[~(2{{x}^{3}}-1)\] and \[(2{{x}^{3}}-2)\] done clear
  View Solution play_arrow

• question_answer27)
  Which of the following is the correct factorization of \[9{{x}^{4}}-40{{x}^{2}}+16?\]
  A)
  \[(2x+1)(x-2)(x+3)(x-7)\] done clear
  B)
  \[(3x+2)(3x-2)(x+2)(x-2)\]                              done clear
  C)
  \[(x-4)(x+2)(x-3)(x+1)\]                           done clear
  D)
  \[(2x-1)(2x+1)(x+1)\left( x-1 \right)\] done clear
  View Solution play_arrow

• question_answer28)
  One of the factors of \[15{{p}^{4}}+3{{p}^{2}}-18\] is equated to 26. Find the integral value of p.                                        
  A)
  \[~\pm \text{ }36\]                                         done clear
  B)
  \[\pm \,3\sqrt{3}\]                          done clear
  C)
  \[~\pm \,2\]                       done clear
  D)
         \[~\pm \,3\]                       done clear
  View Solution play_arrow

• question_answer29)
  Identify the remainder when \[(a{{x}^{2}}+b{{y}^{2}}+b{{x}^{2}}+a{{y}^{2}})\] is divided by \[(a+b)\].
  A)
  1                              done clear
  B)
  0              done clear
  C)
           \[ab\]                    done clear
  D)
         \[{{x}^{2}}{{y}^{2}}\] done clear
  View Solution play_arrow

• question_answer30)
  Identify the four binomials whose product is \[{{({{x}^{2}}-2x)}^{2}}\]\[11({{x}^{2}}+2x)+24.\]
  A)
  \[(x-4),(x+2),(x-3)\] and\[(x+1)\] done clear
  B)
  \[(x+6),(x-2),(x+3)\] and\[(x-1)\] done clear
  C)
  \[(x+4),(x-2),(x+3)\] and\[(x-1)\] done clear
  D)
  \[(x-6),(x+2),(x-3)\] and\[(x+1)\] done clear
  View Solution play_arrow

• question_answer31)
  What are the factors of \[{{x}^{8}}-{{x}^{4}}-30\,\,?\]
  A)
  \[({{x}^{4}}-6)\]and \[({{x}^{4}}-5)\]            done clear
  B)
  \[({{x}^{4}}-6)\] and \[({{x}^{4}}+5)\] done clear
  C)
  \[({{x}^{4}}+6)\] and \[({{x}^{4}}-5)\]            done clear
  D)
  \[({{x}^{4}}+6)\]and \[({{x}^{4}}+5)\] done clear
  View Solution play_arrow

• question_answer32)
  \[8{{(x+y)}^{2}}-10(x+y)-7\]is resolved into factors. Find them.
  A)
  \[(4x-4y-7)\] and\[(2x-2y-\text{ }1)\] done clear
  B)
  \[(4x-4y-7)\]and \[(2x+2y+1)\] done clear
  C)
  \[(4x+4y-7)\] and\[(2x+2y+1)\] done clear
  D)
  \[(4x+4y-7)\] and \[(2x-2y+1)\] done clear
  View Solution play_arrow

• question_answer33)
  If \[(3x-4)(5x+7)=15{{x}^{2}}-ax-28.\]Find the value of a.
  A)
  1                              done clear
  B)
  -1            done clear
  C)
         -2            done clear
  D)
         2 done clear
  View Solution play_arrow

• question_answer34)
  Find the factors of \[{{a}^{5}}-625a.\]
  A)
  \[a({{a}^{2}}-25)(a+5)(a-5)\] done clear
  B)
  \[a({{a}^{2}}+25)(a+5)(a-5)\] done clear
  C)
  \[({{a}^{2}}+25)(a+5)(a-5)\] done clear
  D)
  \[({{a}^{2}}-25)(a+5)(a+5)\] done clear
  View Solution play_arrow

• question_answer35)
  Which of the following is the correct factorization of\[\sqrt{3}{{x}^{2}}+11x+6\sqrt{3}?\]
  A)
  \[(x+3\sqrt{3})(\sqrt{3}x+\sqrt{2})\] done clear
  B)
  \[(x+3\sqrt{3})(\sqrt{3}x+2)\] done clear
  C)
  \[(x-3\sqrt{3})(\sqrt{3}x-\sqrt{2})\] done clear
  D)
  \[(x+\sqrt{3})(x+\sqrt{2})\] done clear
  View Solution play_arrow

• question_answer36)
  The area of a rectangle is\[4{{x}^{4}}-9{{y}^{2}}\]square units. Which of the following factors could represent the length times width?
  A)
  \[(2{{x}^{2}}-3y)(2{{x}^{2}}+3y)\]             done clear
  B)
  \[(2{{x}^{2}}+3y)(2{{x}^{2}}+3y)\] done clear
  C)
  \[(2-3y)(2x-3y)\] done clear
  D)
  \[(2x+3y)(2x-3y)\] done clear
  View Solution play_arrow

• question_answer37)
  Identify one of the factors of \[{{x}^{2}}-11x+24.\]
  A)
  \[x+3\]                                 done clear
  B)
  \[x-3\]                  done clear
  C)
  \[x+4\]                 done clear
  D)
         \[x-4\] done clear
  View Solution play_arrow

• question_answer38)
  \[9{{x}^{2}}+12xy+4{{y}^{2}}-25{{z}^{2}}\]is expressed as a product of two trinomials. Identify it.
  A)
  \[(3x+2y-5z)(3x-2y-5z)\] done clear
  B)
  \[(3x+2y+5z)(3x-2y-5z)\] done clear
  C)
  \[(3x+2y+5z)(3x+2y-5z)\] done clear
  D)
  \[(3x-2y-5z)(3x-2y+5z)\] done clear
  View Solution play_arrow

• question_answer39)
  Find the factors of \[6ax+10y+3bx+5by\] expressed as a product of two binomals.
  A)
  \[(5x+3y)(b+2a)\]            done clear
  B)
  \[(3x+5y)(2a+b)\] done clear
  C)
  \[(x+5y)(a+b)\]      done clear
  D)
            \[(5x+y)(a+3b)\] done clear
  View Solution play_arrow

• question_answer40)
  What is the simplified form of \[\frac{3{{x}^{2}}-9x-54}{x-6}?\]
  A)
  \[3x+5\]                               done clear
  B)
  \[2x+8\]               done clear
  C)
         \[3x+9\]               done clear
  D)
         \[2x+3\] done clear
  View Solution play_arrow