My own word  I think synthetic division is a short cut for long division  Long division is the same as regular long division just doing it with polynomials.

Slides:

Advertisements

Similar presentations

7.4 Remainder and Factor Theorems 7.5 Roots and Zeros

Advertisements

NOTES: FIND POLYNOMIALS OF LEAST DEGREE AND K October 23 rd, 2012.

Warm up Use synthetic division to divide (4x3 – 3x2 + 2x + 1)/ (x – 1) (x3 – x2 – 6)/(x + 2)

Remainder and Factor Theorems

Chapter 6: Polynomials and Polynomial Functions Section 6

EXAMPLE 2 Find the zeros of a polynomial function

EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial function.

Warm-up Find all the solutions over the complex numbers for this polynomial: f(x) = x4 – 2x3 + 5x2 – 8x + 4.

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.)

OBJECTIVES: 1. USE THE FUNDAMENTAL THEOREM OF ALGEBRA 2. FIND COMPLEX CONJUGATE ZEROS. 3. FIND THE NUMBER OF ZEROS OF A POLYNOMIAL. 4. GIVE THE COMPLETE.

Dividing Polynomials Intro - Chapter 4.1. Using Long Division Example 1: Dividing Polynomials DIVISOR DIVIDEND REMAINDER QUOTIENT.

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.

Notes 2.4 –Real Zeros of Polynomial Functions

Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.

Polynomial and Synthetic Division

Ch 2.5: The Fundamental Theorem of Algebra

Concepts 1, 2, Division of Polynomials Division by a Monomial Example:

Polynomial Long Division and Synthetic Division

Long Division Algorithm and Synthetic Division!!!

Synthetic Division 29 October Operations on Polynomials Recap – We know how to: Add Subtract Multiply What about division?

Real Zeros of Polynomial Functions. Quick Review.

5.3 Part 2 Polynomial Division

Chapter 1: Preliminary Information Section 1-4: Polynomials.

Warm-up: 9/9 Factor the following polynomials a.) b.) c.)

Objective Use long division and synthetic division to divide polynomials.

Complex Numbers, Division of Polynomials & Roots.

2.4/2.52.4/2.5 Real Zeros of Polynomial Functions.

Essential Questions How do we use long division and synthetic division to divide polynomials?

Polynomial and Synthetic Division #3. Common Core objectives: * Students will be able to use long division to divide polynomials by other polynomials.

Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.

Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:

6.3 Synthetic Division.

Dividing Polynomials Nicola Breen Nikki Lustrino Kerry Graziosa.

By Ms. Tang. We’ve learned how to solve quadratics (which is a type of polynomials) by: Factoring Completing the square Quadratic formula.

Specialist Maths Polynomials Week 1.

Notes Over 6.5 Using Polynomial Long Division

Warm Up Divide using long division ÷ Divide.

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

Holt Algebra Dividing Polynomials Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients.

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.

Coefficient: a number multiplied by a variable.. Degree: the greatest exponent of its variable.

Quadratic Polynomials by: Kameron Falls. what is a quadratic polynomial A quadratic polynomail is a polynomial of degree 2. A univariate quadratic polynomial.

Objective Use long division and synthetic division to divide polynomials.

Remainder and Factor Theorems

Dividing Polynomials Section 4.3.

Warm-ups Week 8 10/8/12 Find the zeros of f(x) = x3 + 2x2 – 13x + 10 algebraically (without a graphing calculator). What if I told.

Warm Up Compute the following by using long division.

Essential Questions How do we use long division and synthetic division to divide polynomials?

Unit 9: Polynomial Operations

Chapter 6 Polynomials Review

Bell Ringer When solving polynomial equations, what should you do first? 2. How many zeros (roots) will a polynomial have? 3. To get a polynomial.

Lesson 2.5 The Fundamental Theorem of Algebra

Section 3.4 Zeros of Polynomial Functions

Objective Use long division and synthetic division to divide polynomials.

Section 3 – The Remainder and Factor Theorems

Polynomials, Linear Factors, Zeros

Remainder and Factor Theorem

MATH 1310 Section 4.2.

Long Division and Synthetic Division

Warm-up: Find all real solutions of the equation X4 – 3x2 + 2 = 0

Bell Ringer When solving polynomial equations, what should you do first? 2. How many zeros (roots) will a polynomial have? 3. To get a polynomial.

Dividing Polynomials (Long Division)

MATH 1310 Section 4.2.

Dividing Polynomials (Long Division)

By: Jazzae’ Stewart, Kennedy Sanders, and Cebria Webster

Dividing Polynomials (Long Division)

1) Find f(g(x)) and g(f(x) to show that f(x) and g(x) are inverses

Warm Ups: Give the degree, standard form, and leading coefficient (if possible): 1) 3x3 – 5x4 – 10x + 1 2) 9x – 8 + x2 Factor completely: 3) 4x2.

Divide using long division

Warm Up Honors Algebra 2 11/3/17

Presentation transcript:

My own word  I think synthetic division is a short cut for long division  Long division is the same as regular long division just doing it with polynomials.  factor is number that are broken up to # that can be multiply together to get original number.

Factoring  Math Term Definition. Factor. To factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.

Synthetic division  Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

Long division  In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division.

examples of factoring

Examples of long division

Examples Synthetic Division

Step by step Synthetic Division

Step by step long division