Zeros of Polynomial Functions

Which function represents the graph shown, in factored form? 

  $f\left(x\right)=$  

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

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

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

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

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Which function represents a graph with x-intercepts of 3, 5, and -2?

   $f\left(x\right)=$  

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

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

Tags

CCSS.HSA.APR.B.3

State the x-intercepts of the function  $f\left(x\right)=x\left(2x-1\right)\left(3x+1\right)$  . 

Choose ALL that apply.

• $x=0$

• $x=1$

• $x=-1$

• $x=-\frac{1}{3}$

• $x=\frac{1}{2}$

Tags

CCSS.HSA.APR.B.3

State the zeros of the function
 $f\left(x\right)=\left(x+5\right)\left(x-2\right)\left(3x+4\right)$   . 

Choose ALL that apply.

•  $x=5$  

•  $x=-5$  

•  $x=2$  

•  $x=-4$  

•  $x=-\frac{4}{3}$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Given  $\left(x+1\right)$  is a factor of the polynomial  $f\left(x\right)\ =\ 4x^3-12x^2-x+15$  

use synthetic division to help you find 
all of the other factors.  
Choose ALL that apply.

•  $\left(2x-5\right)$  

•  $\left(2x+3\right)$  

•  $\left(2x-3\right)$  

•  $\left(2x+5\right)$  

Tags

CCSS.HSA.APR.B.2

Given  $\left(x-1\right)$  is a factor of the polynomial  $f\left(x\right)=x^3-7x^2-x+7$  

 use synthetic division to rewrite the polynomial in factored form. 

  $f\left(x\right)=$  

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

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

•  $\left(x-1\right)\left(x-6\right)\left(x-1\right)$  

•  $\left(x-1\right)\left(x-6\right)\left(x+1\right)$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.SSE.A.2

Given  $x=-3$  is a zero of the polynomial  $f\left(x\right)\ =\ 2x^3-3x^2-23x+12$  

use synthetic division to find all of the other zeros.  Choose ALL that apply

•  $x=1$  

•  $x=4$  

•  $x=\frac{1}{2}$  

•  $x=-4$  

•  $x=-2$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Given  $x=-3$  is a zero of the polynomial  $f\left(x\right)\ =\ x^3-13x-12$  

use synthetic division to find all of the other zeros.  Choose ALL that apply

•  $x=1$  

•  $x=4$  

•  $x=-1$  

•  $x=-4$  

•  $x=3$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Given that  $x=1$   zero of the function
 $f\left(x\right)=x^3-9x^2+2x+6$  
 use synthetic division to help you find all of the other zeros. All solutions must be exact - no approximate answers.

•  $x=4\pm i\sqrt{10}$  

•  $x=4\pm i\sqrt{22}$  

•  $x=4\pm\sqrt{22}$  

•  $x=-4\pm\sqrt{22}$  

•  $x=-4\pm i\sqrt{10}$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Given that  $x=-2$  is a zero of the function
 $f\left(x\right)=x^3+12x^2+5x-30$  
 
use synthetic division to help you find 
all of the other zeros. 

All solutions must be exact - no approximate answers.

•  $f\left(x\right)=5\pm2\sqrt{10}$  

•  $f\left(x\right)=-5\pm2\sqrt{10}$  

•  $f\left(x\right)=5\pm4\sqrt{10}$  

•  $f\left(x\right)=-5\pm4\sqrt{10}$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3