Fundamental Theorem of Algebra: Explanation and Example

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question 1 of 3

According to the Fundamental Theorem of Algebra, the polynomial function f(x) = x^3 + 5x^2 - x - 5 has how many complex solutions?

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1. The factored form of a polynomial function is f(x) = (x + 4)(x - 2)(x - 1)(x + 1). According to the Fundamental Theorem of Algebra, what is the degree of this function?

2. The following graph is of a polynomial function of degree 2. Are the solutions of this function real or imaginary and why?

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About This Quiz & Worksheet

Learn how to find the number of solutions in a polynomial function with this helpful, easy-to-understand worksheet and quiz set focused on the fundamental theorem of algebra. Our quiz will gauge your ability to solve problems involving polynomial functions and graphs illustrating a function's solutions.

Quiz & Worksheet Goals

These materials on the fundamental theorem of algebra will teach you how to:

  • Define the fundamental theorem and the term complex solutions
  • Find the number of solutions for a polynomial function
  • Graph polynomial functions
  • Determine when a function has repeated solutions
  • Identify when conjugate pairs are present in a function

Skills Practiced

Use the following skills when working with these assets:

  • Problem solving - use acquired knowledge to solve polynomial function practice problems
  • Interpreting information - verify that you can read information regarding imaginary numbers and interpret it correctly
  • Making connections - use understanding of the concept of complex solutions
  • Critical thinking - apply relevant concepts to examine information about the fundamental theorem of algebra in a different light

Additional Learning

Our attached lesson, Fundamental Theorem of Algebra: Explanation and Example, will teach you to:

  • State the fundamental theorem of algebra and explain its purpose
  • Determine the number of solutions in a polynomial function
  • Differentiate real numbers from complex numbers
  • Explain why polynomial functions with real coefficients have imaginary solutions that always occur in conjugate pairs
  • Interpret graphs of polynomial functions
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