partial fractions quiz

Set up the partial fractions...

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CCSS.HSA.APR.D.6

Which one should be used in the partial fraction decomposition of  $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$  

•  $\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$  

•  $\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$  

•  $\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$  

•  $\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$  

Tags

CCSS.HSA.APR.D.6

Which one should be used in the partial fraction decomposition of  $\frac{2x^2-x+4}{x^2-x-2}?$  

•  $2+\frac{-3x}{x^2-x-2}$  

•  $2+\frac{3x}{x^2-x-2}$  

•  $2+\frac{x+8}{x^2-x-2}$  

• none, the fraction is proper

Tags

CCSS.HSA.APR.D.6

 $\int_{ }^{ }\ \ \ \frac{7x}{\left(x-5\right)\left(x+3\right)}$  Which are the equations you get from

• 7=A+B

• 0=A+B

• 7= 3A-5B

• 0= 3A-5B

• none of these are correct

 $\int\frac{2x^2-1}{x^2\left(x-1\right)}dx$  

•  $\ln\left|x\right|-\frac{1}{x}+\ln\left|x-1\right|+C$  

•  $\ln\left|x\right|-\ln(x^2)+\ln\left|x-1\right|+C$  

•  $\ln\left|x\right|+\frac{1}{x}+\ln\left|x-1\right|+C$  

•  $\ln\left|x\right|-\frac{2}{x}-\ln\left|x-1\right|+C$  

 $\int\frac{-2x+3}{4x^2-1}dx$  

•  $\ln|2x-1|-2\ln|2x+1|+C$  

•  $\ln|2x-1|-\ln|2x+1|+C$  

•  $\frac{1}{2}\ln|2x-1|-\ln|2x+1|+C$  

•  $\frac{1}{2}\ln|2x-1|-2\ln|2x+1|+C$  

 $\int\frac{x+2}{6x^2+3x}dx$  

•  $\frac{2}{3}\ln\left|x\right|-\frac{1}{2}\ln\left|2x+1\right|+C$  

•  $2\ln\left|3x\right|-\frac{1}{2}\ln\left|2x+1\right|+C$  

•  $2\ln\left|3x\right|-\ln\left|2x+1\right|+C$  

•  $2\ln\left|3x\right|+\ln\left|2x+1\right|+C$  

 $\int\frac{2}{x^4-1}dx$   which one(s) are NOT a value of the variables

• 1

• -1

• 1/2

• -1/2

• 0

 $\int\frac{2}{x^4-1}dx$  terms in answer include

•  $\frac{1}{2\ }\ln\left|x-1\right|$  
  

•  $\arctan\left(x\right)$  
  

•  $-\frac{1}{2}\ln\left|x+1\right|$ 

•  $\ln\left|x^2+1\right|$  
  

•  $\frac{1}{x-1}$  
  

How are you feeling about partial fractions?

What questions do you still have?

Tags

CCSS.HSA.APR.D.6