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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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