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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)
B)
C)
D)
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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)
B)
C)
D)
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