AnswersPrecalculusPartial Fractions

Partial Fractions — Quiz Answers

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For the expression the fraction with numerator 15 x cubed plus 25 x squared plus 5 x plus 2 and denominator open paren 5 x squared plus 1 close paren squared , which sum represents the correct form of the partial fraction decomposition?

A
the fraction with numerator cap A x plus cap b and denominator open paren 5 x squared plus 1 close paren squared plus the fraction with numerator cap c x plus cap d and denominator open paren 5 x squared plus 1 close paren squared
B
the fraction with numerator cap A and denominator open paren 5 x squared plus 1 close paren squared plus the fraction with numerator cap b and denominator open paren 5 x squared plus 1 close paren squared
C
the fraction with numerator cap A and denominator 5 x squared plus 1 plus the fraction with numerator cap b and denominator open paren 5 x squared plus 1 close paren squared
D
the fraction with numerator cap A x plus cap b and denominator 5 x squared plus 1 plus the fraction with numerator cap c x plus cap d and denominator open paren 5 x squared plus 1 close paren squared
2
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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of the fraction with numerator 7 x squared minus 40 x plus 52 and denominator x squared minus 6 x plus 9 ?

A
cap A plus the fraction with numerator cap b and denominator open paren x minus 3 close paren squared
B
cap A x plus cap b plus the fraction with numerator cap c and denominator x minus 3 plus the fraction with numerator cap d and denominator open paren x minus 3 close paren squared
C
cap A x plus cap b plus the fraction with numerator cap c and denominator open paren x minus 3 close paren squared
D
cap A plus the fraction with numerator cap b and denominator x minus 3 plus the fraction with numerator cap c and denominator open paren x minus 3 close paren squared
3

Which sum represents the partial fraction decomposition of the fraction with numerator 8 x to the 4th power plus 3 x cubed minus 115 x squared minus 39 x plus 200 and denominator 3 x open paren x squared plus 10 close paren squared ?

A
cap A over x plus the fraction with numerator cap b x plus cap c and denominator x squared plus 10 plus the fraction with numerator cap d x plus cap e and denominator open paren x squared plus 10 close paren squared
B
cap A over 3 x plus the fraction with numerator cap b and denominator x squared plus 10
C
cap A over 3 x plus the fraction with numerator cap b x plus cap c and denominator x squared plus 10
D
cap A over x plus the fraction with numerator cap b and denominator x squared plus 10 plus the fraction with numerator cap c and denominator open paren x squared plus 10 close paren squared
4

For the expression the fraction with numerator 2 x squared plus 28 x plus 93 and denominator open paren x plus 6 close paren cubed , which sum represents the correct form of the partial fraction decomposition?

A
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b and denominator open paren x plus 6 close paren squared plus the fraction with numerator cap c and denominator open paren x plus 6 close paren cubed
B
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 6 close paren squared plus the fraction with numerator cap d x squared plus cap e and denominator open paren x plus 6 close paren cubed
C
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 6 close paren squared
D
the fraction with numerator cap A and denominator x plus 6 plus the fraction with numerator cap b and denominator open paren x plus 6 close paren squared
5

Which expression represents the correct form of the partial fraction decomposition of the fraction with numerator 19 x plus 20 and denominator x squared minus 64 ?

A
the fraction with numerator cap A and denominator x minus 8 plus the fraction with numerator cap b and denominator x plus 8
B
the fraction with numerator cap A and denominator x minus 8 plus the fraction with numerator cap b x plus cap c and denominator open paren x minus 8 close paren squared
C
the fraction with numerator cap A x plus cap b and denominator x squared minus 64
D
the fraction with numerator cap A x plus cap b and denominator x squared minus 64 plus the fraction with numerator cap c and denominator x minus 8
6

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of the fraction with numerator 6 x cubed plus 15 x squared plus 20 x plus 36 and denominator 3 x squared plus 7 ?

A
2 x plus the fraction with numerator cap A and denominator 3 x squared plus 7
B
2 x plus the fraction with numerator cap A x plus cap b and denominator 3 x squared plus 7
C
2 x plus 5 plus the fraction with numerator cap A and denominator 3 x squared plus 7
D
2 x plus 5 plus the fraction with numerator cap A x plus cap b and denominator 3 x squared plus 7
7

What is the partial fraction decomposition of the fraction with numerator 7 x squared plus 14 and denominator open paren x squared plus 3 close paren squared ?

A
the fraction with numerator 7 and denominator x squared plus 3 plus the fraction with numerator 7 and denominator open paren x squared plus 3 close paren squared
B
the fraction with numerator 7 and denominator x squared plus 3 minus the fraction with numerator 7 and denominator open paren x squared plus 3 close paren squared
C
the fraction with numerator 7 and denominator x squared plus 3 minus the fraction with numerator 14 and denominator open paren x squared plus 3 close paren squared
D
the fraction with numerator 7 and denominator x squared plus 3 plus the fraction with numerator 14 and denominator open paren x squared plus 3 close paren squared
8

What is the partial fraction decomposition of the fraction with numerator 8 x plus 19 and denominator open paren x plus 8 close paren times open paren x minus 1 close paren ?

A
the fraction with numerator 3 and denominator x plus 8 plus the fraction with numerator 5 and denominator x minus 1
B
the fraction with numerator 11 and denominator x plus 8 plus the fraction with numerator negative 3 and denominator x minus 1
C
the fraction with numerator 5 and denominator x plus 8 plus the fraction with numerator 3 and denominator x minus 1
D
the fraction with numerator negative 3 and denominator x plus 8 plus the fraction with numerator 11 and denominator x minus 1
9

What is the correct form of the partial fraction decomposition for the expression the fraction with numerator 7 x plus 18 and denominator x squared plus 9 x ?

A
the fraction with numerator cap A x plus cap b and denominator x squared plus cap c over 9 x
B
the fraction with numerator cap A and denominator x squared plus cap b over 9 x
C
cap A over x plus the fraction with numerator cap b and denominator x plus 9
D
the fraction with numerator cap A x plus cap b and denominator x plus the fraction with numerator cap c and denominator x plus 9
10

What is the correct form of the partial fraction decomposition for the expression the fraction with numerator 13 x minus 7 and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren ?

A
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b and denominator 4 x minus 3
B
the fraction with numerator cap A and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren plus the fraction with numerator cap b x plus cap c and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren
C
the fraction with numerator cap A and denominator x plus 2 plus the fraction with numerator cap b x plus cap c and denominator 4 x minus 3
D
the fraction with numerator cap A and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren plus the fraction with numerator cap b and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren

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