Polynomial Mixed Review

Polynomial Mixed Review

Multiple Choice

Find all solutions to the polynomial given that (x-1) is a factor. 
 $f\left(x\right)=x^3-14x^2+43x-30$  

• x= 1, 10, 3

• x= -1, 10, 3

• x= 1, -10, 3

• x= 1, -13, 30

Multiple Select

 Find ALL factors of the polynomial given 4 is a solution. $f\left(x\right)=x^3-6x^2+5x+12.$ 

•  $\left(x+4\right)$  

•  $\left(x-4\right)$  

•  $\left(x-3\right)$  

•  $\left(x+1\right)$  

•  $\left(x-2\right)$  

Multiple Choice

Determine the complete factorization of the following polynomial: $f\left(x\right)=x^3+11x^2+31x+21$  

Given that (x+1) is a factor. 

•  $f\left(x\right)=\left(x-1\right)\left(x+3\right)\left(x+7\right)$  

•  $f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x+7\right)$  

•  $f\left(x\right)=\left(x+3\right)\left(x+7\right)$  

•  $x=\ -1,\ -3,\ -7$  

•  $x=\ 1,\ 3,\ 7$  

Multiple Choice

Which word is a synonym for roots?

• zeros

• y-intercept

• maximum

• minimum

Multiple Choice

In the above graph complete the following end behavior:

As x --> -∞, f(x) --> ____

As x --> +∞, f(x) --> ____

• -∞

  -∞

• +∞

  -∞

• -∞

  +∞

• +∞

  +∞

Multiple Choice

What is the absolute minimum point on the polynomial graph?

• There is not an absolute minimum

• (-4,-1.5)

• (-1.5,-4)

• ∞

Multiple Choice

What is the Range of the function being graphed?

• (-∞, ∞)

• [7, ∞)

• (-∞, 7]

• [-1, 1]

Multiple Choice

• $x=2.55,\ -2.55$

• $x=\ -3,\ -2,\ 2,\ 3$

• $x=36$

• $x=2,\ 3$

Open Ended

Find the average rate of change (in simplest form) on the interval

 $3\le x\le5$  .

Multiple Choice

Write a possible equation given the graph:

• $f\left(x\right)=-\left(x+3\right)\left(x-2\right)\left(x-8\right)$

• $f\left(x\right)=\left(x-3\right)\left(x+2\right)\left(x+8\right)$

• $f\left(x\right)=-\left(x+3\right)^2\left(x-2\right)^2\left(x-8\right)^3$

Multiple Choice

Write a possible equation given the graph:

•  $f\left(x\right)=-x\left(x+4\right)\left(x-3\right)$ 

•  $f\left(x\right)=x\left(x+4\right)\left(x-3\right)^2$ 

•  $f\left(x\right)=x\left(x-4\right)\left(x+3\right)$ 

•  $f\left(x\right)=\left(x+4\right)\left(x-3\right)^2$  

Multiple Choice

Write a possible equation given the roots: 2, -5 and 3i.

• $f\left(x\right)=\left(x-2\right)\left(x+5\right)\left(x-3i\right)\left(x+3i\right)$

• $f\left(x\right)=\left(x-2\right)\left(x+5\right)\left(x-3i\right)$

• $f\left(x\right)=\left(x+2\right)\left(x-5\right)\left(x+3i\right)$

• $f\left(x\right)=\left(x+2\right)\left(x-5\right)\left(x+3i\right)\left(x-3i\right)$

Multiple Choice

Write a possible equation given the zeros: -3, 0, and $\sqrt{5}$  

•  $f\left(x\right)=x\left(x-3\right)\left(x+\sqrt{5}\right)$  

•  $f\left(x\right)=x\left(x+3\right)\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)$  

•  $f\left(x\right)=\left(x+3\right)\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)$