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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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