Partial Fractions Sec 4 Revision

 $\frac{8-x}{\left(x+1\right)\left(x-1\right)}$  is a 

• proper fraction

• improper fraction 

• I am not sure

• None of the above

Answer explanation

Yes, since the degree in the numerator is less than the degree in the denominator

If the degree of numerator N(x) is equal or greater than the degree of denominator D(x), then the fraction is:

• proper

• improper

• both proper and improper

• none of the above

Express the following in partial fractions

• 
• 
• 
• 

Which one should be used in the partial fraction decomposition of  $\frac{4x}{\left(x+1\right)\left(3+x^2\right)}?$  

•  $\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x\right)}+\frac{C}{\left(3+x\right)^2}$  

•  $\frac{A}{\left(x+1\right)}+\frac{Bx+C}{\left(3+x^2\right)}$  

•  $\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x^2\right)}$  

•  $\frac{A}{\left(3+x^2\right)}+\frac{Bx}{\left(1+x\right)}$  

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

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

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

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

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

When I need to decompose an improper fraction into its partial fractions, I need to do long division first.

• TRUE

• FALSE

 $\frac{\text{10x-11}}{\text{(x+1)(2x-5)}}=$  

•  $\frac{4}{\left(2x-5\right)}+\frac{3}{\left(x+1\right)}$  

•  $\frac{3}{\left(x+1\right)}+\frac{4}{\left(2x-5\right)}$  

•  $\frac{5}{\left(x+1\right)}+\frac{4}{\left(2x-5\right)}$  

• None of the above

 $\frac{3x-2}{\left(x-1\right)^2}=$  

•  $\frac{A}{\left(x-1\right)}+\frac{Bx+C}{\left(x-1\right)^2}$  

•  $\frac{A}{\left(x-1\right)}+\frac{B}{\left(x-1\right)^2}$  

• I am not sure

Answer explanation

Level 2

 $\frac{7x^2+x+15}{x^3+3x}=$  

•  $\frac{A}{x}+\frac{B}{x^2+3}$  

•  $\frac{A}{x}+\frac{Bx+C}{x^2+3}$  

•  $A+\frac{B}{x}+\frac{C}{x^2+3}$  

•  $Ax+B+\frac{C}{x}+\frac{D}{x^2+3}$  

Answer explanation

Level 3

 $\frac{2x^3-9x^2+7x+8}{\left(2x+1\right)\left(x-2\right)}=$  

•  $Ax+B+\frac{C}{\left(2x+1\right)}+\frac{D}{\left(x-2\right)}$  

•  $\frac{A}{\left(2x+1\right)}+\frac{B}{\left(x-2\right)}$  

• I am not sure

Answer explanation

Level 4, must do long division first to get quotient and remainder