12212021 1 Pre Calculus Santowski LESSON 12 FACTORING

(E) FACTORING POLYNOMIALS – PRACTICE – DAY 2 12/21/2021 g(x) = x 3 +

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 You are given the graph of y =

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 For Pre. Calculus - Santowski the following polynomials,

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 Working with Quartic Polynomials: Pre. Calculus - Santowski

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES Now factor P(x) = -2 x

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES 12/21/2021 If x = 4 is

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES 12/21/2021 You are given the polynomial:

THE RATIONAL ROOT THEOREM EXAMPLES WITHOUT USING TECHNOLOGY, graph f(x) = 3 x 3

HOMEWORK From the textbook Precalculus with Limits – A Graphing Approach (4 th ed)

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12/21/2021 1 Pre. Calculus - Santowski LESSON 12 – FACTORING POLYNOMIALS – DAY 2

(E) FACTORING POLYNOMIALS – PRACTICE – DAY 2 12/21/2021 g(x) = x 3 + 2 x 2 – 16 x – 32 Factor y = x 3 – 9 x 2 + 24 x – 16 Factor f(x) = x 3 – 6 x 2 + 12 x – 8 Factor Pre. Calculus - Santowski Factor g(x) = -x 3 – 2 x 2 + 16 x + 32 2

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 You are given the graph of y = 2 x 3 + 4 x 2 – 3 x – 6. Factor the polynomial and determine all roots Pre. Calculus - Santowski 3

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 For Pre. Calculus - Santowski 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 - 3 x 2 - 2 x + 6 P(x) = x 3 – 4 x 2 – x + 10 y = x 3 + 4 x 2 + 7 x + 6 4

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 You are given the graph of y = 4 x 4 + 4 x 3 – 29 x 2 – 51 x – 18. Factor the polynomial and determine all roots Pre. Calculus - Santowski 5

(E) FACTORING POLYNOMIALS – PRACTICE 12/21/2021 Working with Quartic Polynomials: Pre. Calculus - Santowski Factor P(x) = x 4 – x 3 – 3 x 2 + x + 2 Factor f(x) = x 4 + x 3 – 11 x 2 – 9 x + 18 Factor g(x) = x 4 – 3 x 3 + 6 x 2 – 2 x – 12 For these polynomials, factor the polynomial, solve for the zeroes and then write the equation as a product of linear factors 6

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES Now factor P(x) = -2 x 3 – x 2 + 25 x – 12, making use your work in Ex 1 If x = 4 is root of P(x) = 4 x 3 – 12 x 2 – 19 x + 12, determine the other x-intercepts of P(x) Pre. Calculus - Santowski Factor P(x) = 2 x 3 + x 2 – 25 x + 12, making use of the RRT and the Remainder Theorem 12/21/2021 7

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES 12/21/2021 If x = 4 is root of P(x) = 4 x 3 – 12 x 2 – 19 x + 12, determine the other x-intercepts of P(x) Pre. Calculus - Santowski 8

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM EXAMPLES 12/21/2021 You are given the polynomial: P(x) = 12 x 4 + 32 x 3 – 15 x 2 – 8 x + 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) Pre. Calculus - Santowski 9

THE RATIONAL ROOT THEOREM EXAMPLES WITHOUT USING TECHNOLOGY, graph f(x) = 3 x 3 + x 2 - 22 x - 24 using intercepts, points, and end behaviour. Approximate turning points, max/min points, and intervals of increase and decrease. Pre. Calculus - Santowski SYNTHESIS QUESTION: 12/21/2021 10

HOMEWORK From the textbook Precalculus with Limits – A Graphing Approach (4 th ed) by Larson, Hostetler & Edwards; Sec 2. 3, p 123 -125, Q 3, 17, 23, 25, 31, 37, 41, 48, 54; APP 81; TIPS 87 Pre. Calculus - Santowski Homework: 12/21/2021 11