20.4. Factorization of Polynomials

Try these first

1. 1.

   Define a polynomial.

   Hint

   Think about its general form.

2. 2.

   What does it mean for a polynomial to be irreducible?

   Hint

   Consider what factoring entails.

3. 3.

   What defines an irreducible polynomial?

   • It cannot be factored at all.
   • It can be factored but not into linear factors.
   • It cannot be factored into non-constant polynomials.

   Hint

   Consider what 'factoring' means.

4. 4.

   Is the GCD of two polynomials always unique?

   • True
   • False

   Hint

   Think about how polynomials can be expressed differently.

5. 5.

   Determine if the polynomial 3x^3 + 6x^2 + 3x is reducible or irreducible.

   Hint

   Check for common factors.

6. 6.

   Calculate the GCD of 4x^4 + 8x^2 and 2x^2.

   Hint

   Use polynomial division to find common factors.