Sec. 5.4-5.6 Review Alg. II

Find all roots:
 $x^4-4=0$  

• { $\pm\frac{\sqrt{6}}{3},\ \pm i\sqrt{2}$  }

• { $\pm\frac{i\sqrt{6}}{3},\ \pm i\sqrt{2}$  }

• { $\pm\sqrt{2},\ \pm i\sqrt{2}$  

• { $\pm\sqrt{2},\pm i\sqrt{3}$  }

Solve x⁴ - 256 = 0

• x = 4, x = - 4
• x = 4, x = 4i
• x = 4, x -4, x = 4i
• x = 4, x -4, x = 4i,         x = -4i

Find all roots:
 $x^3-125=0$  

• {5,  $\frac{-5\pm5i\sqrt{3}}{2}$  }

• {5,  $\frac{-5\pm i\sqrt{83}}{2}$  }

• {5, $\frac{-3\pm i\sqrt{91}}{2}$  }

• {5,  $\frac{-3\pm i\sqrt{83}}{2}$  }

Find all roots:
 $x^4-8x=0$  

•  $\left\{0,\ 2,-1\pm i\sqrt{3}\right\}$  

•  $\left\{0,\ 2,\ -1\pm i\sqrt{5}\right\}$  

•  $\left\{0,\ 2,\ -1\pm i\sqrt{2}\right\}$  

•  $\left\{0,\ 1,\ -1\pm i\sqrt{3}\right\}$  

Find all roots:
 $x^3+4x^2-4x-16=0$  

• { $-4,-\frac{2}{3},-2$  }

• { $-4,\ \pm2$ }

• { $-4,\ 2,\ -3$  }

• { $-4,\ 2,\ -\frac{2}{3}$  }

Solve, choose all that apply.

x³ + 2x² + 5x + 10 = 0

• -2

• 2

• -i√5

• i√5

• 0

-2x²+4x+48 ÷ x+4

• -2x+12
• 2x+12
• -4x+9
• 4x+9

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

• 3x³ - 5x² - 2x + 8
• 3x² + x - 6
• 3x² - 5x - 2 + 8/x+1
• 3x³ + x² - 6x