Alg2 Chapter 5 Test

Use Long Division to divide

 $\left(x^3-3x^2+4x+3\right)\div\left(x-2\right)$  

•  $x^2-x+6+\frac{15}{x-2}$  

•  $x^2-x+6-\frac{9}{x-2}$  

•  $x^2-x+2-\frac{1}{x-2}$  

•  $x^2-x-2+\frac{3}{x-2}$  

•  $x^2-x+2+\frac{7}{x-2}$  

 $f\left(x\right)=-2x^4+3x^3-5x+3$  

Evaluate  $f\left(-2\right)$  by synthetic substitution. 

• 38

• -11

• -15

• -43

• 41

 $f\left(x\right)=2x^3-3x^2-17x-12$  
Given  $\left(x-4\right)$  is a factor, find the other two factors.

• (2x-3) and (x+1)

• (2x+3) and (x+1)

• (2x-3) and (x-1)

• (2x+1) and (x+3)

• (2x-1) and (x-3)

Which of these functions has zeros of -2, 1, 3?

• $f\left(x\right)=x^3-2x^2-5x+6$

• $f\left(x\right)=x^3-2x^2+x+6$

• $f\left(x\right)=x^3+2x^2-5x-6$

• $f\left(x\right)=x^3+6x^2-x-6$

• $f\left(x\right)=x^3-4x^2+x-6$

Which of these functions has zeros of -2 and $3i$  

•  $f\left(x\right)=x^3+2x^2-9x-18$  

•  $f\left(x\right)=x^3-2x^2-9x+18$  

•  $f\left(x\right)=x^3+2x^2+9x+18$  

•  $f\left(x\right)=x^3+2x^2+9x-18$  

•  $f\left(x\right)=x^3-2x^2+9x-18$  

 $f\left(x\right)=x^3+8x^2-4x-32$  
How many of each type of roots are there?

Hint:  Factor, find the roots, then count.

• 3 real roots

• 3 imaginary roots

• 1 real root, 2 imaginary roots

• 2 real roots, 1 imaginary root

• 2 real roots, 2 imaginary roots

Describe the end behavior of:
 $f\left(x\right)=-3x^4+6x^3-8x^2+3x-17$  

•  $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

•  $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

•  $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

•  $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

Write the end behavior of the graph.

• $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$
  $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$
  

• $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$
  $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$
  

• $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$
  $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$
  

• $As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$
  $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$
  

Which of these could be a graph of:

 $f\left(x\right)=-2\left(x+1\right)^2\left(x-2\right)$  

• 1

• 2

• 3

• 4

• none of these

Factor

 $8x^3-27$  

•  $\left(2x-3\right)\left(4x^2+6x+9\right)$  

•  $\left(2x+3\right)\left(4x^2-6x+9\right)$  

•  $\left(2x-3\right)\left(4x^2+6x-9\right)$  

•  $\left(2x+3\right)\left(4x^2-6x-9\right)$  

•  $\left(2x-3\right)\left(4x^2-6x+9\right)$