AnswersKISD SS-3401A-Precalculus Honors APartial Fractions

Rational Inequalities Answers

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1
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What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 7 Over x squared + 3 EndFraction minus StartFraction 7 Over (x squared + 3) squared EndFraction
Option A
B
StartFraction 7 Over x squared + 3 EndFraction + StartFraction 7 Over (x squared + 3) squared EndFraction
Option B
C
StartFraction 7 Over x squared + 3 EndFraction minus StartFraction 14 Over (x squared + 3) squared EndFraction
Option C
D
StartFraction 7 Over x squared + 3 EndFraction + StartFraction 14 Over (x squared + 3) squared EndFraction
Option D
2
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What is the quotient and remainder, written as partial fractions, of ?

Question illustration
A
5 + StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option A
B
5 + StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option B
C
5 minus StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option C
D
5 minus StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option D
3

Which sum represents the partial fraction decomposition of ?

Question illustration
A
StartFraction A Over 3 x EndFraction + StartFraction B Over x squared minus 10 EndFraction
Option A
B
StartFraction A Over 3 x EndFraction + StartFraction B x + C Over x squared minus 10 EndFraction
Option B
C
StartFraction A Over 3 x EndFraction + B Over x squared minus 10 EndFraction + StartFraction C Over (x squared minus 10) squared EndFraction
Option C
D
StartFraction A Over 3 x EndFraction + StartFraction B x + C Over x squared minus 10 EndFraction + StartFraction D x + E Over (x squared minus 10) squared
Option D
4

Review the work showing the first few steps in writing a partial fraction decomposition.2x2 + 15x + 19 = A(x + 4)2 + B(x + 4) + C2x2 + 15x + 19 = Ax2 + 8Ax + 16A + Bx + 4B + C

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

For the expression , which sum represents the correct form of the partial fraction decomposition?

Question illustration
A
StartFraction A Over 5 x squared + 1 EndFraction + StartFraction B Over (5 x squared + 1) squared EndFraction
Option A
B
StartFraction A x + B Over 5 x squared + 1 EndFraction + StartFraction C x + D Over (5 x squared + 1) squared EndFraction
Option B
C
StartFraction A Over (5 x squared + 1) squared EndFraction + StartFraction B Over (5 x squared + 1) squared EndFraction
Option C
D
StartFraction A x + B Over (5 x squared + 1) squared EndFraction + StartFraction C x + D Over (5 x squared + 1) squared EndFraction
Option D
6

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 11 Over (x + 1) squared EndFraction
Option A
B
SStartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 17 Over (x + 1) squared EndFraction
Option B
C
StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 11 Over (x + 1) squared EndFraction
Option C
D
StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction minus StartFraction 17 Over (x + 1) squared EndFraction
Option D
7

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 3 Over x + 8 EndFraction + StartFraction 5 Over x minus 1 EndFraction
Option A
B
StartFraction 5 Over x + 8 EndFraction + StartFraction 3 Over x minus 1 EndFraction
Option B
C
StartFraction negative 3 Over x + 8 EndFraction + StartFraction 11 Over x minus 1 EndFraction
Option C
D
StartFraction 11 Over x + 8 EndFraction + StartFraction negative 3 Over x minus 1 EndFraction
Option D
8

What is the correct form of the partial fraction decomposition for the expression ?

Question illustration
A
StartFraction A Over x squared + StartFraction B Over 9 x EndFraction
Option A
B
StartFraction A Over x EndFraction + StartFraction B Over x + 9 EndFraction
Option B
C
StartFraction A x + B Over x squared EndFraction + StartFraction C Over 9 x EndFraction
Option C
D
StartFraction A x + B Over x EndFraction + StartFraction C Over x + 9 EndFraction
Option D
9

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of ?

Question illustration
A
A + StartFraction B Over (x minus 3) squared EndFraction
Option A
B
A x + B + StartFraction C Over (x minus 3) squared EndFraction
Option B
C
A + StartFraction B Over x minus 3 EndFraction + StartFraction C Over (x minus 3) squared EndFraction
Option C
D
A x + B + StartFraction C Over x minus 3 EndFraction + StartFraction D Over (x minus 3) squared EndFraction
Option D
10

For the expression , which sum represents the correct form of the partial fraction decomposition?

Question illustration
A
StartFraction A Over x + 6 EndFraction + StartFraction B Over (x + 6) squared EndFraction
Option A
B
StartFraction A Over x + 6 EndFraction + StartFraction B x + C Over (x + 6) squared EndFraction
Option B
C
StartFraction A Over x + 6 EndFraction + StartFraction B Over (x + 6) squared EndFraction + StartFraction C Over (x + 6) cubed EndFraction
Option C
D
StartFraction A Over x + 6 EndFraction + StartFraction B x + C Over (x + 6) squared EndFraction + StartFraction D x squared + E Over (x + 6) cubed EndFraction
Option D

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