4
2.3 B Remainder and Factor Theorem.notebook 1 September 24, 2013 Sep 1812:52 PM When a polynomial P(x) is divided by (x-k) and there is a remainder, r. ∴P(k) = r Proof: P(x) = Q(x) (x-k) + r when x=k P(k) = Example 1 What is the remainder when x 5 -2x 2 +7 is divided by x-2? A polynomial function P(x) has a factor (x-k) if and only if the remainder is 0. factors of the constant factors of the leading coefficient Remainder Theorem k is the root Factor Theorem the remainder is 0 ∴P(k) =0 Selecting values of k to test 2.3 B Factor and Remainder Theorem

2.3 B Remainder and Factor Theorem.notebookemmell.org/wp...2.3-B-Remainder-and-Factor-Theorem.pdf · What is the remainder when x5-2x2+7 is divided by x-2? A polynomial function P(x)

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 2.3 B Remainder and Factor Theorem.notebookemmell.org/wp...2.3-B-Remainder-and-Factor-Theorem.pdf · What is the remainder when x5-2x2+7 is divided by x-2? A polynomial function P(x)

2.3 B Remainder and Factor Theorem.notebook

1

September 24, 2013

Sep 18­12:52 PM

When a polynomial P(x) is divided by (x-k) and there is a remainder, r.

∴P(k) = r

Proof: P(x) = Q(x) (x-k) + rwhen x=k

P(k) =

Example 1 What is the remainder when x 5-2x2+7 is divided by x-2?

A polynomial function P(x) has a factor (x-k) if and only if the remainder is 0.

factors of the constant

factors of the leading coefficient

Remainder Theorem

k is the root

Factor Theoremthe remainder is 0

∴P(k) =0

Selecting values of k to test

2.3 B Factor and Remainder Theorem

Page 2: 2.3 B Remainder and Factor Theorem.notebookemmell.org/wp...2.3-B-Remainder-and-Factor-Theorem.pdf · What is the remainder when x5-2x2+7 is divided by x-2? A polynomial function P(x)

2.3 B Remainder and Factor Theorem.notebook

2

September 24, 2013

Sep 18­12:53 PM

Example 2 Factor Fully

a)

b)

Choose factors of the constant to substitute using factor theorem. Trial and error until you find the remainder of 0.

Always try to factor before using factor theorem

Page 3: 2.3 B Remainder and Factor Theorem.notebookemmell.org/wp...2.3-B-Remainder-and-Factor-Theorem.pdf · What is the remainder when x5-2x2+7 is divided by x-2? A polynomial function P(x)

2.3 B Remainder and Factor Theorem.notebook

3

September 24, 2013

Sep 18­12:57 PM

Determine the values of m and n so that the polynomials 2x3+mx2+nx-3 and x3-3mx2t2nx+4 are both divisible by x-2

Example 3

Page 4: 2.3 B Remainder and Factor Theorem.notebookemmell.org/wp...2.3-B-Remainder-and-Factor-Theorem.pdf · What is the remainder when x5-2x2+7 is divided by x-2? A polynomial function P(x)

2.3 B Remainder and Factor Theorem.notebook

4

September 24, 2013

Sep 18­12:53 PM

p.177#3,4ace,6ab,7be,9,10,11,

Homework


Long Division of Polynomials - baroody.org 2/2.3 Notes (filled in).pdf · Section 2.3 - Long/Synthetic Division and the Remainder & Factor Theorems Synthetic Division of Polynomials

Long Division of Polynomials - baroody.org 2/2.3 Notes (filled in).pdf · Section 2.3 - Long/Synthetic Division and the Remainder & Factor Theorems Synthetic Division of Polynomials

Documents
1 Remainder and Factor Theorem - La Sierra Universityfaculty.lasierra.edu/~jvanderw/classes/m121a16res/ch3notesans.pdf · Math 121. Practice Problems from Chapter 3 Fall 2016 1 Remainder

1 Remainder and Factor Theorem - La Sierra Universityfaculty.lasierra.edu/~jvanderw/classes/m121a16res/ch3notesans.pdf · Math 121. Practice Problems from Chapter 3 Fall 2016 1 Remainder

Documents
A1: 99 Problems Remainder & Factor Theorems Easy Question

A1: 99 Problems Remainder & Factor Theorems Easy Question

Documents
13 Synthetic, Remainder and Factor Theorem

13 Synthetic, Remainder and Factor Theorem

Documents
2.3 Long and Synthetic Division of polynomials · Vocab: long division, synthetic division, remainder theorem, factor theorem, divisor, quotient, dividend, remainder Objectives: to

2.3 Long and Synthetic Division of polynomials · Vocab: long division, synthetic division, remainder theorem, factor theorem, divisor, quotient, dividend, remainder Objectives: to

Documents
Section 4-3 The Remainder and Factor Theorems. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant,

Section 4-3 The Remainder and Factor Theorems. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant,

Documents
The Factor & Remainder Theorems - Solutions

The Factor & Remainder Theorems - Solutions

Documents
Remainder Factor Theorems May 27 2009

Remainder Factor Theorems May 27 2009

Education
2.5 Apply the Remainder and Factor Theorems p. 120

2.5 Apply the Remainder and Factor Theorems p. 120

Documents
Remainder and Factor Theorem Day 1 - Mrs. Allison's BLOG...Remainder Theorem: If a polynomial f (x) is divided by x — k , then the remainder, r , is r f (This connects synthetic

Remainder and Factor Theorem Day 1 - Mrs. Allison's BLOG...Remainder Theorem: If a polynomial f (x) is divided by x — k , then the remainder, r , is r f (This connects synthetic

Documents
Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Documents
Factor/Remainder theorem and quadratic theory - … ·  · 2015-02-02Factor/Remainder theorem and quadratic theory ... Examples are 3x3,3x3-1,3x2 + 2x, ... (x + 1) is a factor of

Factor/Remainder theorem and quadratic theory - … ·  · 2015-02-02Factor/Remainder theorem and quadratic theory ... Examples are 3x3,3x3-1,3x2 + 2x, ... (x + 1) is a factor of

Documents
Elementary Hydrostatics - The Maths Mann...Remainder theorem: if a polynomial f(.r) is divided by PX + q, the remainder is if divided by x — a, the remainder is f(a). Factor theorem:

Elementary Hydrostatics - The Maths Mann...Remainder theorem: if a polynomial f(.r) is divided by PX + q, the remainder is if divided by x — a, the remainder is f(a). Factor theorem:

Documents
Remainder and Factor Theorem

Remainder and Factor Theorem

Documents
REMAINDER AND FACTOR THEOREM… · Find the Remainder by using the Factor Theorem . 14x3 – 12x2 – 5x + 3 by x – 1 Find the Remainder by using the Factor Theorem . When 2x3 –

REMAINDER AND FACTOR THEOREM… · Find the Remainder by using the Factor Theorem . 14x3 – 12x2 – 5x + 3 by x – 1 Find the Remainder by using the Factor Theorem . When 2x3 –

Documents
Polynomial Factors Polynomial Factor Theorem. 7/23/2013 Polynomial Factors 2 The Remainder Theorem Polynomial f(x) divided by x – k yields a remainder

Polynomial Factors Polynomial Factor Theorem. 7/23/2013 Polynomial Factors 2 The Remainder Theorem Polynomial f(x) divided by x – k yields a remainder

Documents
remainder and factor theorem ms - WordPress.com · Obtain linear factor 2x— 1 Obtain linear factor x + 3 [Condone omission of repetition that x— 2 is a factor. I [If linear factors

remainder and factor theorem ms - WordPress.com · Obtain linear factor 2x— 1 Obtain linear factor x + 3 [Condone omission of repetition that x— 2 is a factor. I [If linear factors

Documents
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

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

Documents
Section 3.1: The Remainder and Factor Theorems 135... · The Factor Theorem The number c is a zero of a polynomial, P(x), iff x-c is a factor of P(x). Section 3.1 The Remainder and

Section 3.1: The Remainder and Factor Theorems 135... · The Factor Theorem The number c is a zero of a polynomial, P(x), iff x-c is a factor of P(x). Section 3.1 The Remainder and

Documents
Dividing Polynomials; Remainder and Factor Theorems... · 3.3 Dividing Polynomials; Remainder and Factor Theorems Objectives: •Use long division to divide polynomials. •Use synthetic

Dividing Polynomials; Remainder and Factor Theorems... · 3.3 Dividing Polynomials; Remainder and Factor Theorems Objectives: •Use long division to divide polynomials. •Use synthetic

Documents
Factor and Remainder Theorem

Factor and Remainder Theorem

Education
The Remainder and Factor Theorems - Mr. Schwartz's …czschwartz.weebly.com/uploads/2/1/4/0/21406690/chapter_2-3... · The Remainder and Factor Theorems You factored quadratic expressions

The Remainder and Factor Theorems - Mr. Schwartz's …czschwartz.weebly.com/uploads/2/1/4/0/21406690/chapter_2-3... · The Remainder and Factor Theorems You factored quadratic expressions

Documents
The Remainder and Factor Theorems Check for Understanding 3103.3.21 – Factor polynomials using a variety of methods including the factor theorem, synthetic

The Remainder and Factor Theorems Check for Understanding 3103.3.21 – Factor polynomials using a variety of methods including the factor theorem, synthetic

Documents
Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Documents
Polynomial Functions Characteristics The Remainder Theorem The Factor Theorem Equations and Graphs Math

Polynomial Functions Characteristics The Remainder Theorem The Factor Theorem Equations and Graphs Math

Documents
5.4 Notes Synthetic Division, Remainder Theorem, and Factor Theorem

5.4 Notes Synthetic Division, Remainder Theorem, and Factor Theorem

Documents
MHF 4U Lesson 2.0 Review of Factoring Ex. Factor each of ... · MHF 4U Lesson 2.2 The Factor and Remainder Theorems The Remainder Theorem The remainder theorem states: When a polynomial

MHF 4U Lesson 2.0 Review of Factoring Ex. Factor each of ... · MHF 4U Lesson 2.2 The Factor and Remainder Theorems The Remainder Theorem The remainder theorem states: When a polynomial

Documents
Remainder and Factor Theorem.ppt

Remainder and Factor Theorem.ppt

Documents
Explain how the Remainder Theorem and the Factor Theorem … ·  · 2015-09-01Explain how the Remainder Theorem and the Factor ... examples: l. What is the remainder when f(x) by

Explain how the Remainder Theorem and the Factor Theorem … ·  · 2015-09-01Explain how the Remainder Theorem and the Factor ... examples: l. What is the remainder when f(x) by

Documents
The Remainder and Factor Theorems

The Remainder and Factor Theorems

Documents