9th Class Mathematics Polynomials Question Bank

done Polynomials Total Questions - 25

• question_answer1)
  The value of k for which \[(x+2)\] is a factor of (x \[{{(x+1)}^{7}}+{{(3x+k)}^{3}}\] is ____.
  A)
   -7                                done clear
  B)
   7                     done clear
  C)
   -1                    done clear
  D)
         \[-6-{{3}^{(7/3)}}\]                  done clear
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• question_answer2)
  The remainder when \[{{x}^{4}}-{{y}^{4}}\]is divided by \[x-y\]is ____.
  A)
   0                     done clear
  B)
         \[x+y\]  done clear
  C)
   \[{{x}^{2}}-{{y}^{2}}\]        done clear
  D)
         \[2{{y}^{4}}\] done clear
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• question_answer3)
  When \[p(x)={{x}^{3}}+a{{x}^{2}}+2x+a\]is divided by \[(x+a).\] the remainder is ___.
  A)
   0                     done clear
  B)
          a         done clear
  C)
   -a                    done clear
  D)
          2a        done clear
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• question_answer4)
  \[{{x}^{12}}-{{y}^{12}}=\]
  A)
  \[(x-y)({{x}^{2}}+xy+{{y}^{2}})(x+y)({{x}^{2}}-xy+{{y}^{2}})\]\[({{x}^{2}}+{{y}^{2}})({{x}^{4}}-{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] done clear
  B)
  \[(x+y)({{x}^{2}}-xy+{{y}^{2}})(x+y)({{x}^{2}}-xy+{{y}^{2}})\]\[({{x}^{2}}+{{y}^{2}})({{x}^{4}}-{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] done clear
  C)
  \[(x+y)({{x}^{2}}+xy-{{y}^{2}})(x+y)({{x}^{2}}-xy+{{y}^{2}})\]\[({{x}^{2}}+{{y}^{2}})({{x}^{4}}-{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] done clear
  D)
   \[(x-y)({{x}^{2}}-xy+{{y}^{2}})(x+y)({{x}^{2}}-xy+{{y}^{2}})\]\[({{x}^{2}}+{{y}^{2}})({{x}^{4}}-{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] done clear
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• question_answer5)
  If \[X=\frac{a-b}{a+b}.y=\frac{b-c}{b+c},Z=\frac{c-a}{c+a},\]then the value of \[\frac{(1+x)(1+y)(1+z)}{(1-x)(1-y)(1-z)}\]is _______.
  A)
   \[abc\]                          done clear
  B)
  \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]     done clear
  C)
          1                     done clear
  D)
         \[-1\] done clear
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• question_answer6)
  If \[(x+2)\] and\[(x-1)\]are factors of \[({{x}^{3}}+10{{x}^{2}}+3x+n),\]then the value of m, n respectively are _______.
  A)
   -5, 5                             done clear
  B)
   7, 18    done clear
  C)
          7,-18                done clear
  D)
          -5,-18   done clear
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• question_answer7)
  Given that \[x=2\]is a solution of \[{{x}^{3}}-7x+6=0.\]The other solutions are_____.
  A)
   -1, 3                             done clear
  B)
   1,-3                  done clear
  C)
   1,-2                  done clear
  D)
          -1,-2     done clear
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• question_answer8)
  If \[(x+k)\] is a common factor of \[f(x)=({{x}^{2}}+px+q)\]and\[g(x)=({{x}^{2}}+lx+m),\]then the value of k is ____.
  A)
  \[l+p\]                           done clear
  B)
  \[m-q\]   done clear
  C)
         \[\frac{l-p}{m-q}\]          done clear
  D)
         \[\frac{m-q}{l-p}\]          done clear
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• question_answer9)
  The product\[(a+b)(a-b)({{a}^{2}}-ab+{{b}^{2}})\]\[({{a}^{2}}+ab+{{b}^{2}})\] is equal to ___.
  A)
   \[{{a}^{6}}+{{b}^{6}}\] done clear
  B)
   \[{{a}^{6}}-{{b}^{6}}\] done clear
  C)
   \[{{a}^{3}}-{{b}^{3}}\] done clear
  D)
   \[{{a}^{3}}+{{b}^{3}}\] done clear
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• question_answer10)
  The value of \[{{(x-a)}^{3}}+{{(x-b)}^{3}}+{{(x-c)}^{3}}\]\[-3(x-a)(x-b)(x-c),\]when \[a+b+c=3x\]is ______.
  A)
   3                                 done clear
  B)
   2         done clear
  C)
   1                     done clear
  D)
          0 done clear
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• question_answer11)
  Value of R, if \[\frac{{{a}^{2}}-19a-25}{a-7}=a-12+\frac{R}{a-7}\]is _____.
  A)
   -109                             done clear
  B)
   -88                   done clear
  C)
   -84                   done clear
  D)
          -64 done clear
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• question_answer12)
  When \[({{x}^{3}}-2{{x}^{2}}+px-q)\] is divided by \[({{x}^{2}}-2x-3),\]the remainder is\[(x-6).\]The values of p and q respectively are
  A)
   -2,-6                             done clear
  B)
   2,-6                  done clear
  C)
   -2, 6                 done clear
  D)
          2, 6                  done clear
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• question_answer13)
  Find the remainder when the expression \[3{{x}^{3}}+8{{x}^{2}}-6x+1\] is divided by \[x+3.\]
  A)
   1                                 done clear
  B)
   10                    done clear
  C)
   6                     done clear
  D)
          0 done clear
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• question_answer14)
  If \[{{x}^{2}}-1\]is a factor of \[a{{x}^{4}}+b{{x}^{3}}+e{{x}^{2}}+dx+e,\] then
  A)
  \[a+b+e=c+d\] done clear
  B)
  \[a+b+c=d+e\] done clear
  C)
  \[b+c+d=a+e\] done clear
  D)
   None of these done clear
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• question_answer15)
  If a, b, c are all non-zeroes and \[a+b+c=0,\]then \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}=\_\_\_\_\_.\]
  A)
   0                     done clear
  B)
          1                     done clear
  C)
   2                                 done clear
  D)
   3 done clear
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• question_answer16)
  Length, breadth and height of a cuboidal tank are \[(x-3y)m,\,(x+3y)m\]and\[({{x}^{2}}+9{{y}^{2}})m\]  respectively. Find the volume of the tank.
  A)
  \[({{x}^{3}}+3xy+27{{y}^{3}}){{m}^{3}}\] done clear
  B)
  \[({{x}^{4}}+2{{x}^{2}}{{y}^{2}}+81{{y}^{4}}){{m}^{3}}\] done clear
  C)
  \[({{x}^{2}}-81{{y}^{4}}){{m}^{3}}\]  done clear
  D)
  \[({{x}^{4}}+81{{y}^{4}}){{m}^{3}}\] done clear
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• question_answer17)
  A rectangular field has an area \[(35{{x}^{2}}+13x-12){{m}^{2}}.\]What could be the possible expression for length and breadth of the field?
  A)
  \[(5x+4)\]and\[(7x-3)m\] done clear
  B)
  \[(3x+9)m\]and\[(7x-12)m\] done clear
  C)
   Both (a) and (b) done clear
  D)
   None of these done clear
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• question_answer18)
  Santosh has Rs. \[({{x}^{3}}-3{{x}^{2}}+4x+50).\]He want to buy chocolates each of cost Rs.\[(x-3).\] After buying maximum number of chocolates with his money, how much money is left with him?
  A)
   Rs. 50              done clear
  B)
   Rs. 40 done clear
  C)
          Rs. 62              done clear
  D)
          Rs. 20 done clear
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• question_answer19)
  Area of a rectangular field is \[(2{{x}^{3}}-11{{x}^{2}}-4x+5)\,sq.\]units and side of a square field is (\[(2{{x}^{2}}+4)\]units. Find the difference between their areas (in sq. units).
  A)
  \[4{{x}^{4}}-2{{x}^{3}}-4x+11\] done clear
  B)
  \[4{{x}^{4}}-2{{x}^{3}}+27{{x}^{2}}+4x+11\] done clear
  C)
  \[4{{x}^{4}}+27{{x}^{2}}+4x-11\] done clear
  D)
  \[4{{x}^{4}}+2{{x}^{3}}+27{{x}^{2}}+4x+11\]    done clear
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• question_answer20)
  Vikas has Rs. \[({{x}^{3}}+2ax+b),\] with this money he can buy exactly \[(x-1)\] jeans or\[(x+1)\] shirts with no money left. How much money Vikas has, if\[x=4?\]
  A)
   Rs. 80                          done clear
  B)
   Rs. 120 done clear
  C)
          Rs. 30              done clear
  D)
          Rs. 60 done clear
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• question_answer21)
  Which of the following statements is INCORRECT?
  A)
   Every non-zero constant polynomial has zero roots. done clear
  B)
   Zero polynomial has zero root. done clear
  C)
   Every linear polynomial has exactly one root. done clear
  D)
   If\[x-a\]is the root of \[p(x)=0,\]then \[p(a)=0,\] done clear
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• question_answer22)
  If \[{{(5{{x}^{2}}+14x+2)}^{2}}-{{(4{{x}^{2}}-5x+7)}^{2}}\]is divided by \[({{x}^{2}}+x+1),\] then quotient 'q' and remainder '/-' respectively, are ____.
  A)
  \[({{x}^{2}}+19x-5),0\] done clear
  B)
  \[9({{x}^{2}}+19x-5),0\] done clear
  C)
  \[({{x}^{2}}+19x-5),1\] done clear
  D)
  \[9({{x}^{2}}+19x-5),1\] done clear
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• question_answer23)
  Select the CORRECT statement.
  A)
   If \[x=\frac{\sqrt{3}+1}{\sqrt{3}-1}+\frac{\sqrt{3}-1}{\sqrt{3}+1}+\frac{\sqrt{3}-2}{\sqrt{3}+2},\]then value of \[{{x}^{2}}+{{\left( \frac{39}{x} \right)}^{2}}\]is 110. done clear
  B)
   Every integer is a whole number. done clear
  C)
   Between two rational numbers, there exist infinite number of integers. done clear
  D)
   None of these done clear
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• question_answer24)
  Match the following.

  Column - I	Column - II
  (p) If\[f(x)={{x}^{3}}-6{{x}^{2}}+11x-6,\] then \[f(-1)=\_\_\_.\]	(i) \[-210\]
  (q) If \[f(x)=2{{x}^{3}}-13{{x}^{2}}+17x+12,\]then \[f(-3)=\_\_\_\_.\]	(ii) 1
  (r) if \[x=\frac{4}{3}\]is a root of \[f(x)=6{{x}^{3}}-11{{x}^{2}}+kx-20,\]then \[k=\_\_\_\_.\]	(iii) \[-24\]
  (s) If \[x=-1\]is a root of \[f(x)={{x}^{100}}+2{{x}^{99}}+k,\]then \[k=\_\_\_.\]	(iv) 19

  A)
              \[(p)\to (iii);(q)\to (iv);(r)\to (i);(s)\to (ii)\] done clear
  B)
         \[(p)\to (ii);(q)\to (iv);(r)\to (i);(s)\to (iii)\] done clear
  C)
              \[(p)\to (iii);(q)\to (i);(r)\to (iv);(s)\to (ii)\] done clear
  D)
              \[(p)\to (iii);(q)\to (ii);(r)\to (i);(s)\to (iv)\] done clear
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• question_answer25)
  Study the given statements.

  Statement I: \[\frac{{{({{a}^{2}}-{{b}^{2}})}^{3}}+{{({{b}^{2}}-{{c}^{2}})}^{3}}+{{({{c}^{2}}-{{a}^{2}})}^{3}}}{{{(a+b)}^{3}}{{(b+c)}^{3}}+{{(c+a)}^{3}}}\]

  Statement II:  \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca\]            \[=\frac{1}{2}\left[ {{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}} \right]\]

  Which of the following options holds?
  A)
   Both Statement-I and Statement-II are true. done clear
  B)
   Statement-I is true but Statement-II is false. done clear
  C)
   Statement-I is false but Statement-II is true. done clear
  D)
   Both Statement-I and Statement-II are false. done clear
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