Polynomial Functions Test (2.1-2.5)

Solve by factoring. Write your solutions as x=___, x=___.

x² + 5x = 14

Solve by completing the square:  $x^2+6x+2=0$  

•  $x=3\pm\sqrt{7}$   

•  $x=-3\pm\sqrt{7}$  

• no real solutions

•  $x=3\pm\sqrt{2}$  

•  $x=-3\pm\sqrt{2}$  

Solve by using the quadratic formula. $\frac{2}{x}+\frac{4}{x^2}=5$  

• no real solutions

•  $\frac{2\pm\sqrt{76}}{10}$  

•  $\frac{1\pm2\sqrt{21}}{5}$  

•  $\frac{1\pm\sqrt{21}}{5}$  

The quadratic function with no real roots is represented by graph #____.

The quadratic function with a double root is represented by graph #____.

• 4, 1 or 3

• 2, 1 or 3

• 2, 4

• 4, 2

• none of these

Write a quadratic function representing this graph.  

•  $f\left(x\right)=-\frac{6}{5}\left(x+1\right)\left(x-5\right)$  

•  $f\left(x\right)=-\frac{6}{5}\left(x-1\right)\left(x+5\right)$  

•  $f\left(x\right)=\frac{6}{5}\left(x+1\right)\left(x-5\right)$  

•  $f\left(x\right)=\frac{6}{5}\left(x-1\right)\left(x+5\right)$  

• none of these

Simplify: $\left(3-5i\right)^2$   

• -16

• 34

• -16-30i

• 34-30i

Simplify: $\frac{5}{3-\sqrt{6}}$   

•  $5+5\sqrt{2}$  

•  $15+\sqrt{2}$  

•  $\frac{15+\sqrt{6}}{3}$  

•  $\frac{15+5\sqrt{6}}{3}$  

Simplify: $i\sqrt{50}-\sqrt{-18}$   

•  $i\cdot5\sqrt{2}-3i$  

•  $i\ \cdot\ 2\sqrt{2}$  

• cannot be simplified

• none of these

Write the equation of a polynomial of least degree with roots x = -2 and x = 3+2i. Leave in factored form.

Write the equation for the polynomial shown here. Leave your equation in factored form.