1. Solving Polynomials

2. Factoring Options 1.GCF Factoring (take-out a common term) 2.Sum or Difference of Cubes 3.Factor by Grouping 4.U Substitution 5.Polynomial Division (to factor out a binomial term)

3. Take-out common monomial (GCF Factoring) 1) 2)

4. Sum or Difference of Cubes 1.Solve 2.Solve

5. Factor by Grouping 3) 4)

6. Solving an Equation of Quadratic Type (“U” Substitution) 5) 6)

7. Synthetic Division Use synthetic division to find the quotient and the remainder when is divided by x – 2. If x – 2 is a factor, then factor the polynomial completely. How can we determine whether x – 2 is a factor?

8. Factor Theorem A polynomial f(x) has a factor x – a iff the remainder is 0.

9. Example 1 Use synthetic division to determine whether x – 1 is a factor of x³ - 1.

10. Example 2 x = -4 is a solution of x³ - 28x – 48 = 0. Use synthetic division to factor and find all remaining solutions.

11. Example 3 x + 3 is a factor of y = 3x³ + 2x² - 19x + 6. Find all the zeros of this polynomial.

12. Rational Roots (Zeros) Test Every rational zero that is possible for a given polynomial can be expressed as the factors of the constant term divided by the factors of the leading coefficient.

13. Example 4 List all possible rational roots for the polynomial y = 10x³ - 15x² - 16x + 12. Then, divide out the factor and solve for all remaining zeros.

14. Example 5 List all possible rational roots for the polynomial y = x³ - 7x – 6. Then, divide out the factor and solve for all remaining zeros.

15. Practice Pg. 213 (53 – 67 odd, 68) Pg. 278 (41, 43, 55, 57, 59)