1. LESSON 12 – FACTORING POLYNOMIALS – DAY 2 PreCalculus - Santowski 10/20/2015 1 PreCalculus - Santowski

2. (E) FACTORING POLYNOMIALS – PRACTICE – DAY 2 Factor g(x) = x 3 + 2x 2 – 16x – 32 Factor y = x 3 – 9x 2 + 24x – 16 Factor f(x) = x 3 – 6x 2 + 12x – 8 Factor g(x) = -x 3 – 2x 2 + 16x + 32 10/20/2015 2 PreCalculus - Santowski

3. (E) FACTORING POLYNOMIALS – PRACTICE 10/20/2015 PreCalculus - Santowski 3 You are given the graph of y = 2x 3 + 4x 2 – 3x – 6. Factor the polynomial and determine all roots

4. (E) FACTORING POLYNOMIALS – PRACTICE For the following polynomials, factor the polynomial, solve for the zeroes and then write the equation as a product of linear factors P(x) = x 3 - 3x 2 - 2x + 6 P(x) = x 3 – 4x 2 – x + 10 y = x 3 + 4x 2 + 7x + 6 10/20/2015 4 PreCalculus - Santowski

5. (E) FACTORING POLYNOMIALS – PRACTICE 10/20/2015 PreCalculus - Santowski 5 You are given the graph of y = 4x 4 + 4x 3 – 29x 2 – 51x – 18. Factor the polynomial and determine all roots

6. (E) FACTORING POLYNOMIALS – PRACTICE Working with Quartic Polynomials: Factor P(x) = x 4 – x 3 – 3x 2 + x + 2 Factor f(x) = x 4 + x 3 – 11x 2 – 9x + 18 Factor g(x) = x 4 – 3x 3 + 6x 2 – 2x – 12 For these polynomials, factor the polynomial, solve for the zeroes and then write the equation as a product of linear factors 10/20/2015 6 PreCalculus - Santowski

7. (E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM - EXAMPLES Factor P(x) = 2x 3 + x 2 – 25x + 12, making use of the RRT and the Remainder Theorem Now factor P(x) = -2x 3 – x 2 + 25x – 12, making use your work in Ex 1 If x = 4 is root of P(x) = 4x 3 – 12x 2 – 19x + 12, determine the other x-intercepts of P(x) 10/20/2015 7 PreCalculus - Santowski

8. (E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM - EXAMPLES If x = 4 is root of P(x) = 4x 3 – 12x 2 – 19x + 12, determine the other x-intercepts of P(x) 10/20/2015 8 PreCalculus - Santowski

9. (E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM - EXAMPLES You are given the polynomial: P(x) = 12x 4 + 32x 3 – 15x 2 – 8x + 3, And you know that x + 3 is a factor of P(x) and that x = ½ is a zero of P(x). Find the other zeroes of P(x) 10/20/2015 9 PreCalculus - Santowski

10. (E) FACTORING POLYNOMIALS – THE RATIONAL ROOT THEOREM - EXAMPLES SYNTHESIS QUESTION: WITHOUT USING TECHNOLOGY, graph f(x) = 3x 3 + x 2 - 22x - 24 using intercepts, points, and end behaviour. Approximate turning points, max/min points, and intervals of increase and decrease. 10/20/2015 10 PreCalculus - Santowski

11. H OMEWORK Homework: From the textbook Precalculus with Limits – A Graphing Approach (4 th ed) by Larson, Hostetler & Edwards; Sec 2.3, p123-125, Q3,13,17,23,25,31,37,41,48,54; APP  81; TIPS  87 10/20/2015 11 PreCalculus - Santowski