Polynomial functions - finding zeros and writing equations

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.

•  $\left(2x-5\right)$  

•  $\left(2x+3\right)$  

•  $\left(2x-3\right)$  

•  $\left(2x+5\right)$  

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.

•  $x=5$  

•  $x=-5$  

•  $x=2$  

•  $x=-4$  

•  $x=-\frac{4}{3}$  

Which function represents the graph shown, in factored form? 

  $f\left(x\right)=$  

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

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

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

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

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

•  $x=1$  

•  $x=4$  

•  $x=-1$  

•  $x=-4$  

•  $x=3$  

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.

•  $f\left(x\right)=5\pm2\sqrt{10}$  

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

•  $f\left(x\right)=5\pm4\sqrt{10}$  

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

Find a polynomial function of degree 3 with zeros 3i and -2.

• P(x) = x³+2x²+9x+11
• P(x) = x³-2x²+9x+18
• P(x) = x³+2x²+9x+18
• P(x) = x²-3ix+2x-6i

How many zeros does the polynomial function
 P(x) = 3x⁴+4x-8 have?

• 1
• 2
• 3
• 4