23.1.1. Definition of Roots

Try these first

1. 1.

   Define what a root of a polynomial is.

   Hint

   Think about where the polynomial crosses the x-axis.

2. 2.

   What is the maximum number of roots a polynomial of degree 3 can have?

   Hint

   Consider the degree definition.

3. 3.

   What is a root of a polynomial?

   • A value where f(x)=1
   • A value where f(x)=0
   • The highest degree term

   Hint

   Think about where the polynomial touches the x-axis.

4. 4.

   True or False: The degree of a polynomial limits the number of roots it can have.

   • True
   • False

   Hint

   Recall definitions surrounding polynomial properties.

5. 5.

   Prove that a quadratic polynomial can have at most 2 roots.

   Hint

   Consider the nature of square roots.

6. 6.

   Factor the polynomial f(x) = x^3 - 3x^2 + 4x - 12 completely.

   Hint

   Start with possible rational roots and use synthetic division.