Warmup 9-17 1.Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.

Slides:



Advertisements
Similar presentations
7.4 Remainder and Factor Theorems 7.5 Roots and Zeros
Advertisements

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.
Warm up Use synthetic division to divide (4x3 – 3x2 + 2x + 1)/ (x – 1) (x3 – x2 – 6)/(x + 2)
Problem of the Day. Division and Rational Root Theorem TS: Making decisions after reflection and review Obj: Review polynomial division and how to find.
5.5: Polynomial Long Division and Synthetic Division
Unit 3 Practice Test Review. 1a) List all possible rational zeros of this polynomial: 5x 4 – 31x x 2 – 31x + 6 p  1, 2, 3, 6 q  1, 5 p  1, 2,
Chapter solving Equations by Multiplying or dividing
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
5.5 Apply the Remainder and Factor Theorem
Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.
Synthetic Division. This method is used to divide polynomials, one of which is a binomial of degree one.
EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. – – 8 5 – 6 15 – 21 2 – 5 7 – 16 2x 3 + x 2.
Rational Root Theorem By: Yu, Juan, Emily. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.
6.6 The Fundamental Theorem of Algebra
Homework Lesson 2.3 Read: Pages Page 127: #1-61 (EOO)
Ch 2.5: The Fundamental Theorem of Algebra
Section 2.3 Polynomial and Synthetic Division Long Division of polynomials Ex. (6x 3 -19x 2 +16x-4) divided by (x-2) Ex. (x 3 -1) divided by (x-1) Ex (2x.
Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.
Warm-Up 2/
Algebraic long division Divide 2x³ + 3x² - x + 1 by x + 2 x + 2 is the divisor The quotient will be here. 2x³ + 3x² - x + 1 is the dividend.
1. Describe the end behavior of the graph y = 2x 5 – 3x Sketch a graph of 3 rd degree with a zero at -5 (multiplicity 2) and a zero at 0 (multiplicity.
Using the Fundamental Theorem of Algebra 6.7. Learning Targets Students should be able to… -Use fundamental theorem of algebra to determine the number.
Complex Numbers, Division of Polynomials & Roots.
4.3: Real Zeroes of Polynomials Functions February 13, 2008.
Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.
The Remainder Theorem A-APR 2 Explain how to solve a polynomial by factoring.
Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.
To play click Back to menu A B A C B A D C B A D C B D C A B C D Simplifying Factor Factor/ Dividing Misc Back to menu D C B A Mixed Review D.
Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.
Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:
X + 5 4x +20x R + 3 3x x Tues 11/24 Lesson 5 – 4 Learning Objective: To divide polynomials by synthetic division Hw: Pg.
Solving Polynomials. What does it mean to solve an equation?
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 =
Solving Polynomial Functions involving Complex Numbers.
Algebra Review: Solving Quadratic Equations by Factoring.
quotient () () () ()
Polynomial and Synthetic Division Objective: To solve polynomial equations by long division and synthetic division.
SYNTHETIC DIVISION SYNTHETIC DIVISION IS USED TO FIND THE QUOTIENT AND REMAINDER OF THE POLYNOMIAL. JAYASHREE AGASTI.
Solving Polynomials. 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.
5.1 – 5.6 Review Algebra 2. Exponents! Evaluate the expression: ∙ (x 3 y -5 )(x 2 y) 2 3.(3x 3 y 6 ) -2.
PRE-CALCULUS UNIT 2: POWER AND POLYNOMIAL FUNCTIONS REVIEW.
Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:
Unit 3.3- Polynomial Equations Continued. Objectives  Divide polynomials with synthetic division  Combine graphical and algebraic methods to solve polynomial.
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
Algebra Finding Real Roots of Polynomial Equations.
Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.
Dividing Polynomials Two options: Long Division Synthetic Division.
Goal: to divide polynomials using LONG and SYNTHETIC methods.
3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x
Divide by x - 1 Synthetic Division: a much faster way!
Chapter 6 Polynomials Review
Please log on to your computers.
When given a root and when not given a root
Rational Root Theorem and Fundamental Theorem of Algebra
1a. Divide using long division. (9x3 – 48x2 + 13x + 3) ÷ (x – 5)
2.5 Zeros of Polynomial Functions
Rational Root Theorem and Fundamental Theorem of Algebra
Chapter 5 Polynomials Describe Graphs Synthetic Division
Notes 5.6 (Day 1) Find Rational Zeros.
Apply the Remainder and Factor Theorems
WARMUP 2 (
Factor Theorems.
Remainder and Factor Theorem
Apply the Fundamental Theorem of Algebra
Dividing Polynomials (Long Division)
Warm UP: Factor Completely: 1)16n3 + 32n2 – n – 2 2) y4 – 3y2 – 28
Solving Special Cases.
Warm Up.
Presentation transcript:

Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show work! (9x 4 - 9x x 2 + 1x + 30) ; -5 2.Find all zeroes for the following polynomial. Show work! x 3 + 6x x List all possible zeroes for the following polynomial. 6x x x + 21

Algebra 2 Review Factoring and finding zeroes Factor completely. Show work 1.27x x x 2 – x 2 – 36x x 2 – 17x x 3 – 60x x 2 + 3x – 108. x 3 - 6x x For #9-11, divide using synthetic division. Then factor the remaining equation completely and solve for x. Show work! 9. (x x 2 – 34x - 280)  (x + 4) 10. (4x 3 – 47x x -84)  ( x – 7) 11. 4x x x - 30)  (x - 6)

Algebra 2 Review Factoring and finding zeroes In each problem below, a polynomial and one of its zeroes is given. Use the zero given to divide using synthetic division. Then factor the remaining polynomial completely AND find the remaining zeroes. Show work! 12. (x 3 - 8x x – 180); (6x 3 – 37x x - 24); (x x x – 144); -2 List all possible zeroes for the following polynomials 15. x 3 – 14x x – x x 2 -19x x x 2 +12x + 20 In #18-20 below, find all zeroes for each polynomial given. Show work! 18. x 3 – 15x x x x x – x 3 – 10x x + 30