1. 4.3: Real Zeroes of Polynomials Functions February 13, 2008

2. Objectives Divide polynomials Understand the division algorithm, remainder theorem, and factor theorem Factor higher degree polynomials Analyze polynomials with multiple zeroes Find rational zeros Solve polynomial equations

3. Divide polynomials Divide by a monomial (3x 3 +6x 2 +7)/(2x) Dividing by binomials or higher (2x 3 +4x 2 -x+6)/(x+1)

4. Understand the division algorithm, remainder theorem, and factor theorem Division algorithm: f(x) = d(x) * q(x) + r(x) Remainder theorem if f(x) is divided by x-k, the remainder is f(k) Factor theorem f(x) has x-k as a factor if and only if f(k)=0

5. Ways to factor polynomials functions Graphically– see where the zeros are Using synthetic algebra– if you know one zero (k), factor out x-k Factor out x if possible

6. If you know the zeros f(x)= a(x-c 1 )(x-c 2 )… etc f(x)= 2x 2 -25x+77 Zeros 11/2 and 7

7. Your assignment Page 288-292 –16-22 even –36, 38