23.2.2.1. Possibilities of Factors

Try these first

1. 1.

   What is a root of a polynomial?

   Hint

   Look for where f(x) = 0.

2. 2.

   What is the degree of the polynomial 3x^4 - 2x^2 + 7?

   Hint

   Identify the highest power of x in the polynomial.

3. 3.

   What does a polynomial root signify?

   • It means the polynomial has been factored.
   • It is a value that makes the polynomial equal zero.
   • It refers to the degree of the polynomial.

   Hint

   Recall the relationship defined by the factor theorem.

4. 4.

   True or false: A polynomial of degree n can have more than n roots.

   • True
   • False

   Hint

   Think about the relationship between degree and factors.

5. 5.

   Given the polynomial f(x) = x^5 - 32, find its roots and confirm how many roots it has.

   Hint

   Use the rational root theorem for finding potential roots.

6. 6.

   Demonstrate how to factor the polynomial x^6 + 1 and identify its irreducible factors.

   Hint

   Look for patterns or known factorizations.