HM3 2.3/2.4A Rational Expressions: Proper or Improper?

Is the rational function proper or improper?

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

• proper

• improper

Is the rational function proper or improper?

 $f\left(x\right)=\frac{3x^2-2x+7}{x^5-5}$  

• proper

• improper

Is the rational function proper or improper?

 $f\left(x\right)=\frac{x^3+4x^2+2x}{10x+7}$  

• proper

• improper

Is the rational function proper or improper?

 $f\left(x\right)=\frac{5x^2-4x+4}{7x^5-2x+3}$  

• proper

• improper

Is the rational function proper or improper?

 $f\left(x\right)=\frac{\left(x+1\right)}{\left(x-2\right)\left(x+2\right)}$  

• proper

• improper

Divide the expression and rewrite it such that

 $\frac{a\left(x\right)}{b\left(x\right)}=q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$  .

 $\frac{x^2-6x-1}{x+3}$  

•  $x-9+\frac{-28}{x+3}$  

•  $x-9+\frac{26}{x+3}$  

•  $x-3+\frac{8}{x+3}$  

•  $x-3+\frac{-10}{x+3}$  

Divide the expression and rewrite it such that  $\frac{a\left(x\right)}{b\left(x\right)}=q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$  .

 $\frac{x^3-5x+2}{x-10}$  

•  $x^2-10x+95+\frac{-948}{x+10}$  

•  $x+5+\frac{52}{x-10}$  

•  $x-15+\frac{152}{x+10}$  

•  $x^2+10x+95+\frac{952}{x-10}$  

Divide the expression and rewrite it such that $\frac{a\left(x\right)}{b\left(x\right)}=q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$  

 $\frac{5x-8}{x-4}$  

•  $5+\frac{12}{x-4}$  

•  $5+\frac{-28}{x-4}$  

•  $5x+\frac{12}{x-4}$  

•  $5x+\frac{-28}{x-4}$  

Divide the expression and rewrite it such that $\frac{a\left(x\right)}{b\left(x\right)}=q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$  

 $\frac{2x^3-7x^2+6}{x-3}$  

•  $2x^2-13x+39+\frac{-111}{x-3}$  

•  $2x^2-x-3+\frac{-3}{x-3}$  

•  $2x-1+\frac{3}{x-3}$  

•  $2x-13+\frac{45}{x-3}$