Warm Up no 0, 3 x = -3. Homework Questions Section 2.2 Synthetic Division; The Remainder and Factor Theorems Objective: To use synthetic division and.

Slides:

Advertisements

Similar presentations

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

Advertisements

5.3 Division of Polynomials. Dividing a Polynomial by a monomial.  Divide each term of the polynomial by the monomial.

Section 5.4 Dividing Polynomials. Review of Long Division What terms do we use to describe 672 and 21? Because the reminder is zero, we know that 21 is.

Unit 3 Practice Test Review. Page 9 (back) 5) List all possible rational zeros of this polynomial: 5x 4 – 31x x 2 – 31x + 6 p  1, 2, 3, 6 q  1,

Pre Calc Lesson 2.2 Synthetic Division ‘Remainder’ and ‘Factor’ Theorems Review Long Division: 5365 ÷ 27 Now review ‘long division’ of polynomials: (2x.

7.1 Synthetic Division & the Remainder & Factor Theorems

5.5 Apply the Remainder and Factor Theorem

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.

2.2 D IVIDING POLYNOMIALS ; R EMAINDER AND F ACTOR T HEOREMS.

5.4 – Apply the Remainder and Factor Theorems Divide 247 / / 8.

Polynomial Division and the Remainder Theorem Section 9.4.

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.

7.4 THE REMAINDER & FACTOR THEOREMS Objectives: The student will be able to… 1)evaluate functions using synthetic substitution 2)determine whether a binomial.

1 Warm-up Determine if the following are polynomial functions in one variable. If yes, find the LC and degree Given the following polynomial function,

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

ACTIVITY 31: Dividing Polynomials (Section 4.2, pp )

6-7 The Division Algorithm & The Remainder Theorem dividend=quotient. divisor + remainder If a polynomial f(x) is divided by x - c, the remainder is the.

 The remainder theorem states that the remainder that you get when you divide a polynomial P(x) by (x – a) is equal to P(a).  The factor theorem is.

quotient is x + 6 and remainder is quotient is x.

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.

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,

If a polynomial f(x) is divided by (x-a), the remainder (a constant) is the value of the function when x is equal to a, i.e. f(a). Therefore, we can use.

Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.

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

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

Help the Poor Math Student  Vocabulary Dividend: number being divided Divisor: number you are dividing by Quotient: is number you get when you divide.

a. b.  To simplify this process, we can use a process called division.  Synthetic division works when dividing a polynomial by.  To get started, make.

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?

7.6 Rational Zero Theorem Depressed equation. All the possible rational Zeros To find all the possible rational zero, take all the factors of the last.

Finding Roots With the Remainder Theorem. Dividing Polynomials Remember, when we divide a polynomial by another polynomial, we get a quotient and a remainder.

quotient () () () ()

Lesson 11-2 Remainder & Factor Theorems Objectives Students will: Use synthetic division and the remainder theorem to find P(r) Determine whether a given.

Section 4.3 Polynomial Division; The Remainder and Factor Theorems Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

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

Warm – up #2 Find the remainder when P(x) is divided by x – c.

Long and Synthetic Division. Long Division Polynomial long division can be used to divide a polynomial d(x), producing a quotient polynomial q(x) and.

6.5 Warm Up 1.Factor 8x Factor 5x x 2 – x – 2. 3.Factor 200x 6 – 2x 4. 4.Find the product of (2x – 3)(2x – 5). 5.Find the product of (5x.

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.

3.2 Division of Polynomials. Remember this? Synthetic Division 1. The divisor must be a binomial. 2. The divisor must be linear (degree = 1) 3. The.

Dividing Polynomials Section 4.3.

Dividing Polynomials Two options: Long Division Synthetic Division.

Divide x3 + x2 – 10x + 8 by x+4 using long 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.

Section 5.4 – Dividing Polynomials

Section 3.2 Dividing Polynomials (std Alg 2 3.0)

Dividing Polynomials Long Division A little review:

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

Dividing Polynomials Algebra

Multiplying and Dividing Polynomials

5.2 The Factor Theorem & Intermediate Value Theorem

Apply the Remainder and Factor Theorems

Honors Precalculus February 10, 2017 Mrs. Agnew

Honors Precalculus February 21, 2018 Mr. Agnew

Remainder and Factor Theorem

Long Division and Synthetic Division

Chapter 2 notes from powerpoints

Multiplying and Dividing Polynomials

Section 2.4: Real Zeros of Polynomial Functions

21 = P(x) = Q(x) . (x - r) + P(r) 4.3 The Remainder Theorem

2.5 Apply the Remainder and Factor Theorem

Divide using long division

3.2 The Remainder Theorem.

Presentation transcript:

Warm Up no 0, 3 x = -3

Homework Questions

Section 2.2 Synthetic Division; The Remainder and Factor Theorems Objective: To use synthetic division and to apply the remainder and factor theorems.

Vocabulary When 23 is divided by 4, the quotient is 5 and the remainder is 3. 4 is not a factor of 23, because if when 23 is divided by 4 the remainder is not zero.

The Remainder Theorem When a polynomial P(x) is divided by x – a, the remainder is P(a) Remainder =P(a)

2-2 Synthetic Division; The Remainder and Factor THMs

Example 1 Divide P(x) = x 3 + 5x 2 + 5x – 2, by x + 2

The Factor Theorem if and only if

Example 4 If P(x) = 2x 4 + 5x 3 – 8x 2 – 17x – 6, determine whether each of the following is a factor of P(x): A) x – 1 B) x – 2

Example 3 If x = -1 is a root, find all others roots for p(x)= x 3 + 3x 2 + x – 1

Classwork Class Exercises Page 60 #1-5

Homework Section 2.2 Page 61 #1-25 odds