Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all roots for this function? |
b. f(x) has three real roots. |

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? |
a. -9i |

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots? |
fx = (3x^2 – 4x -5)(2x^6 – 5) |

If f(x) is a third degree polynomial function, how many distinct complex roots are possible? |
a. 0 or 2 |

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x^7 – x^5 + x^3 + 6 |
c. 7 roots |

Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-√2i, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true? |
d. Patricia is not correct because both 3 – 4i and -11+√2i must be roots. |

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 |
b. 3 roots |

Which of the following statements must be true about the polynomial function f(x)? |
b. If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x). |

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots? |
b. f(x) = (x + 2)^3 (x^2 – 7x + 3)^4 |

Which of the following describes the roots of the polynomial function f(x) = (x – 3)^4 (x + 6)^2? |
d. 3 with multiplicity 4 and -6 with multiplicity 2 |

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x^5 – 3x |
d. 5 roots |

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots? |
d. f(x) = 7x^6 + 3x^3 + 12 |

How many x intercepts appear on the graph of this polynomial function? |
b. 2 x intercepts |

# The Fundamental Theorem of Algebra

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