Remainder Theorem Long Division. Long Division Question Divide the following.

Slides:

Advertisements

Similar presentations

Remainder and Factor Theorems

Advertisements

© 2007 M. Tallman. - - Step 1: Divide (÷) Step 2: Multiply (×) Step 3: Subtract (-) Step 4: Bring Down ( ↓ ) Step 5: Repeat or Remainder ) 43 5 How many.

5.5 Apply the Remainder and Factor Theorem

Bell Problem Find the real number solutions of the equation: 18x 3 = 50x.

HW: Pg #13-61 eoo.

6.8 Synthetic Division. Polynomial Division, Factors, and Remainders In this section, we will look at two methods to divide polynomials: long division.

Polynomial Division, Factors, and Remainders ©2001 by R. Villar All Rights Reserved.

2.5 Apply the Remainder and Factor Theorems p. 120 How do you divide polynomials? What is the remainder theorem? What is the difference between synthetic.

Polynomial Division and the Remainder Theorem Section 9.4.

6.5 The Remainder and Factor Theorems p. 352 How do you divide polynomials? What is the remainder theorem? What is the difference between synthetic substitution.

1 Algebra 2: Section 6.5 The Remainder and Factor Theorems (Day 1)

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.

1 What we will learn today…  How to divide polynomials and relate the result to the remainder and factor theorems  How to use polynomial division.

Real Zeros of Polynomial Functions

3.2 Dividing Polynomials 11/28/2012. Review: Quotient of Powers Ex. In general:

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

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.

Long Division Synthetic Division Remainder Theorem Can only divide by x-a.

The Remainder and Factor Theorems 6.5 p When you divide a Polynomial f(x) by a divisor d(x), you get a quotient polynomial q(x) with a remainder.

2.3 Polynomial Division and Synthetic Division Ex. Long Division What times x equals 6x 3 ? 6x 2 6x x 2 Change the signs and add x x.

Warm Up 9-1 Use long division to find the quotient and remainder for the problems below ÷ ÷ 4.

6-5: The Remainder and Factor Theorems Objective: Divide polynomials and relate the results to the remainder theorem.

Section 5.3(d) Synthetic Substitution. Long division Synthetic Division can be used to find the value of a function. This process is called Synthetic.

Section 2-2 Synthetic Division; The Remainder and Factor Theorems.

7.3 Products and Factors of Polynomials Objectives: Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.

Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.

3.6 Day 2 Why Synthetic Division? What use is this method, besides the obvious saving of time and paper?

Using theorems to factor polynomials.  If a polynomial f(x) is divided by x-k, then the remainder r = f(k)  This is saying, when you divide (using synthetic.

Synthetic Division and Zeros. Synthetic division Only applies when the divisor is x-c and when every descending power of x has a place in the dividend.

2.5 Apply the Remainder and Factor Theorem Long Division and Synthetic Division Pg. 85.

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

DIVIDING POLYNOMIALS Mr. Richard must have your “Un-Divided” attention for this lesson!

Polynomial & Synthetic Division Algebra III, Sec. 2.3 Objective Use long division and synthetic division to divide polynomials by other polynomials.

WARM UP. Homework Q’s Dividing Polynomials using Synthetic Division EQ: How is Long Division utilized to divide a polynomial functions? Assessment:

X + 5 4x +20x R + 3 3x x Tues 11/24 Lesson 5 – 4 Learning Objective: To divide polynomials by synthetic division Hw: Pg.

Real Zeros of Polynomials Section 2.4. Review – Long Division 1. What do I multiply by to get the first term? 2. Multiply through 3. Subtract 4. Bring.

WARM UP 1. Factor the polynomial completely. 27 – y 3 2. What are the real number solutions of the equation 2x = x 2 + x 3 ?

2.5 – Apply the remainder and factor theorems

Notes Over 6.5 Using Polynomial Long Division

5.6 The Remainder and Factor Theorems. [If you are dividing by (x - 6), the remainder will be the same as if you were evaluating the polynomial using.

Quotient Dividend Remainder Divisor Long Division.

Sect. 2-2 Synthetic Division; The remainder and Factor theorems Objective: SWBAT use the synthetic division and to apply the remainder and factor theorems.

Pre Calculus – Synthetic Division Unit 3. First, you have to write the coefficients of the polynomial to be divided at the top (remember to use 0’s.

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.

Polynomial Division Objective: To divide polynomials by long division and synthetic division.

Factor Theorem. Remainder Theorem When a function f(x), is divided by x – k the remainder is f(k) Example 1.

Polynomial & Synthetic Division Algebra III, Sec. 2.3 Objective Use long division and synthetic division to divide polynomials by other polynomials.

Bellwork 1)Use the quadratic formula to solve 2)Use synthetic substitution to evaluate for x = 2 3) A company’s income is modeled by the function. What.

Dividing Polynomials Section 4.3.

Dividing Polynomials Two options: Long Division Synthetic Division.

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.

3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x

#2.5 Long Division.

1a. Divide using long division. (9x3 – 48x2 + 13x + 3) ÷ (x – 5)

Dividing Polynomials Algebra

Dividing Polynomials Tyler McKell.

DIVIDING POLYNOMIALS Synthetically!

6.5 The Remainder and Factor Theorems

Real Zeros of Polynomial Functions

5.5 - Long and Synthetic Division

Remainder and Factor Theorem

5.5 Apply the Remainder and Factor Theorems

Today in Precalculus Go over homework Notes: Remainder

6.5 The Remainder and Factor Theorems

The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

5.5 Apply the Remainder and Factor Theorems

Warm Up Honors Algebra 2 11/3/17

Dividing Polynomials (SYNTHETIC Division)

Presentation transcript:

Remainder Theorem Long Division

Long Division Question Divide the following

Long Division How many times does x go into x 3 ? Multiply x-3 by x 2. Subtract down. Note 4x 2 – (-3x 2 )=4x 2 + (+3x 2 )=7x 2 Bring down +2x. How many times does x go into 7x 2 ? Multiply x-3 by 7x. Subtract down. Bring down –5. How many times does x go into 23x ? Multiply x-3 by 23. Subtract down.

See textbook pg 85 for Computer Algebra System division

Synthetic Division The division statement is: To find the remainder without doing the division we could substitute 3 into the function. You try one (see Notebook)

Remainder Theorem When a function f(x), is divided by x – k the remainder is f(k) Example 1

Example 2