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

Slides:

Advertisements

Similar presentations

Notes 6.6 Fundamental Theorem of Algebra

Advertisements

Rational Functions Characteristics. What do you know about the polynomial f(x) = x + 1?

Plowing Through Sec. 2.4b with Two New Topics: Homework: p odd Remainder and Factor Theorems with more Division Practice.

This is JEOPARDY!!! It would be wise to be attentive, take appropriate notes, and ask questions.

2.4 – Zeros of Polynomial Functions

1.5 - Factoring Polynomials - The Factor Theorem MCB4U - Santowski.

Remainder and Factor Theorem Unit 11. Definitions Roots and Zeros: The real number, r, is a zero of f(x) iff: 1.) r is a solution, or root of f(x)=0 2.)

Section 6-2: Polynomials and Linear Factors

WRITING LINEAR EQUATIONS FINDING THE X-INTERCEPT AND Y- INTERCEPT.

Factor Theorem & Rational Root Theorem

1.6 - Solving Polynomial Equations MCB4U - Santowski.

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

Copyright © 2011 Pearson, Inc. 2.4 Real Zeros of Polynomial Functions.

6.9 – Modeling with Polynomial Functions

Factors, Remainders, and Roots, Oh My! 1 November 2010.

Today in Pre-Calculus Go over homework Notes: Remainder and Factor Theorems Homework.

Do Now Let 1. Which of the given polynomials is a factor of f(x)?

Polynomials, Factors and Zeros

Section 2.4 Dividing Polynomials; The Factor and Remainder Theorems.

Chapter 6-3 Dividing Polynomials (std Alg 2 3.0) Objectives: To understand long division of polynomials To understand synthetic division of polynomials.

12/17/2015 Math 2 Honors - Santowski 1 Lesson 22 – Solving Polynomial Equations Math 2 Honors - Santowski.

7.4 Solving Polynomial Equations

Lesson 19 – Factoring Polynomials Math 2 Honors - Santowski 12/23/20151Math 2 Honors - Santowski.

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

5.2 Polynomials, Linear Factors, and Zeros P

Lesson 20 – Algebra of Polynomials – Intro to Factoring Math 2 Honors - Santowski 1/5/20161Math 2 Honors - Santowski.

Lesson 12 – Factoring Polynomials PreCalculus - Santowski 1/5/20161 PreCalculus - Santowski.

4.4 The Rational Root Theorem

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

Lesson 12 – Working with Polynomial Equations

1/14/2016 Math 2 Honors - Santowski 1 Lesson 20 – Solving Polynomial Equations Math 2 Honors - Santowski.

1/27/2016 Math 2 Honors - Santowski 1 Lesson 21 – Roots of Polynomial Functions Math 2 Honors - Santowski.

This is JEOPARDY!!! It would be wise to be attentive, take appropriate notes, and ask questions.

5.2 Polynomials, Linear Factors, and Zeros

Solving Polynomials.

Solving polynomial equations

Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

LESSON 14 – FUNDAMENTAL THEOREM of ALGEBRA PreCalculus - Santowski.

TRASHKETBALL PRECALCULUS CHAPTER 2 QUIZ. WHAT IS THE VERTEX AND WHAT ARE THE INTERCEPTS?

Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:

PreCalculus 4-R Unit 4 Polynomial and Rational Functions Review Problems.

Find the roots Identify the multiplicity 3.5: Finding Real Roots of Polynomial Equations.

Last Answer LETTER I h(x) = 3x 4 – 8x Last Answer LETTER R Without graphing, solve this polynomial: y = x 3 – 12x x.

HOMEWORK CHECK.

Factor Theorem & Rational Root Theorem

Lesson 23 – Roots of Polynomial Functions

4.1 Notes day 2 Remainder Theorem: If a polynomial f(x) is divided by x – c, then the remainder is f(c). Ex. f(x) = x3 + 3 divided by g(x)= x -1.

4.2 Real Zeros Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0. Zero, solution, root.

Finding Real Roots of Polynomial Equations

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

5-5 Theorems About Roots of Polynomial Equations

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

Algebra II with Trigonometry Ms. Lee

Lesson 13 – Working with Polynomial Equations

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Today in Precalculus Go over homework Notes: Remainder

Factor Theorem & Rational Root Theorem

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Factor Theorem & Rational Root Theorem

Warm Up Identify all the real roots of each equation.

3.6 Polynomial Functions Part 2

Warm Up Use long division to find (6

Warm Up Identify all the real roots of each equation.

Warm UP: Factor Completely: 1)16n3 + 32n2 – n – 2 2) y4 – 3y2 – 28

8-5 Rational Zero Theorem

5 Minute Check 1-4 Graph the equation : 2x + y – 4 = 0

Preview to 6.7: Graphs of Polynomial

The Real Zeros of a Polynomial Function

Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts

Presentation transcript:

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

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

(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

(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 /20/ PreCalculus - Santowski

(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

(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/ PreCalculus - Santowski

(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 x – 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/ PreCalculus - Santowski

(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/ PreCalculus - Santowski

(E) FACTORING POLYNOMIALS – THE REMAINDER THEOREM - EXAMPLES You are given the polynomial: P(x) = 12x x 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/ PreCalculus - Santowski

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

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