1. Real Zeros of Polynomials Section 2.4

2. Review – Long Division 1. What do I multiply by to get the first term? 2. Multiply through 3. Subtract 4. Bring down next term

4. CONCLUSION

7. Review: Synthetic Division 1. Solve the divisor for “x” 2. Set up problem with coefficients ONLY 3. Bring down the first term 4. Multiply, add, repeat

10. FACTOR THEOREM (x – k) is a factor of a polynomial if and only if f(k) = 0

11. Practice  Determine whether each binomial is a FACTOR of f(x) = x 3 + 3x 2 – 6x – 8 1. (x – 2) 2. (x + 3) 3. (x + 4)

17. Rational Zeros Theorem  Rational #s – numbers that can be written as fractions  POSSIBLE rational zeros of a polynomial can be found by dividing the factors of the LAST TERM and LEADING COEFFICIENT

18. Practice – find possible rational zeros f(x) = 3x 3 + 4x 2 – 5x – 2 Factors of -2: Factors of 3: 1, -1, 2, -2 1, -1, 3, -3 1, -1, 2, -2

19. List all of the POSSIBLE rational zeros of f(x) = 2x 3 – x 2 – 9x + 9

20. PUTTING IT ALL TOGETHER 1. Find all of the zeros (rational & irrational) f(x) = 2x 3 – 3x 2 – 4x + 6 Step 1: List possible rational zeros Step 2: Find one from the list that IS a zero Step 3: Synthetic Division Step 4: Factor

21. Ticket Out 1.) Is 2x + 1 a factor of 4x 3 - 8x 2 – 1 ? Show work 2.) Divide x 3 – 5x 2 + 3x – 2 by (x + 1) using LONG division 3.) Divide x 3 – 5x 2 + 3x – 2 by (x + 1) using SYNTHETIC 4.) List all possible rational zeros of f(x) = 2x 4 + 3x – 3