1. What is the relationship between the FOIL method of multiplying two binomials, and getting the same product by ╥long multiplication╙ (multiplication written vertically)?
2. Can you make any prediction about the degree of the PRODUCT of two polynomials? What if you multiply a polynomial of degree two and one of degree three -- can you predict the degree of the product? What about polynomials of degree m and n?
3. Think again about the degree of the ╥zero╙ polynomial (consisting of just the constant number 0). When the zero polynomial is multiplied by a polynomial of degree 2 (say, x-squared), the product is zero. What is the degree of the product? What is the rule for the degree of any product? Do you see any trouble with the degree of the zero polynomial?
