What is synthetic division?

Slides:

Advertisements

Similar presentations

6.3 Dividing Polynomials. Warm Up Without a calculator, divide the following Solution:

Advertisements

5.5 Apply the Remainder and Factor Theorem

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.)

2.2 Remainder and Factor Theorems 1 Remainder Theorem If the polynomial f(x) is divided by x  c, then the remainder is equal to f(c). In other words,

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

Do Now: Factor the following polynomial:. By the end of this chapter, you will be able to: - Identify all possible rational zeroes - Identify all actual.

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# Long Division Polynomials

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem

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

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.

Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.

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

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

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.

ACTIVITY 31: Dividing Polynomials (Section 4.2, pp )

 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.

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.

UNIT 2, LESSON 4 THEOREMS ABOUT ZEROS. GETTING STARTED Find the quotient and remainder when is divided by x-3.

Snapshot of the School Year Algebra 2 Honors Class Alex Asemota Mrs. Vittese Period 4 May 3, 2012.

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?

The Remainder Theorem A-APR 2 Explain how to solve a polynomial by factoring.

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.

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

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.

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

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.

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

Remainder and Factor Theorems

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.

Homework Questions?.

#2.5 Long Division.

Divide by x - 1 Synthetic Division: a much faster way!

Pre-Calculus Section 2.3 Synthetic Division

Long & Synthetic Division

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

4.1 Notes day 2 Remainder Theorem: If a polynomial f(x) is divided by x – c, then the remainder is f(c). Ex. f(x) = x3 + 3 divided by g(x)= x -1.

6.3 Dividing Polynomials.

2.5 Zeros of Polynomial Functions

5.8 Rational Zero Theorem.

Solving Fractional Equations

Packet #8 Dividing Polynomials

Apply the Remainder and Factor Theorems

Polynomial Division; The Remainder Theorem and Factor Theorem

Homework Questions?.

Essential Question: How do I divide polynomials?

Section 3 – The Remainder and Factor Theorems

Remainder and Factor Theorem

Today in Precalculus Go over homework Notes: Remainder

Homework Check.

Long Division and Synthetic Division

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

What is synthetic division?

3.6 Polynomial Functions Part 2

What is synthetic division?

What is synthetic division?

Warm UP: Factor Completely: 1)16n3 + 32n2 – n – 2 2) y4 – 3y2 – 28

What is synthetic division?

2.5 Apply the Remainder and Factor Theorem

n n – 1 f (x) = an x n + an – 1 x n – 1 +· · ·+ a 1 x + a 0 a 0 a0

7.1 Synthetic Division & the Remainder & Factor Theorems

Dividing Polynomials (SYNTHETIC Division)

Presentation transcript:

Essential Question: How do I use synthetic division to find all of the zeros? What is synthetic division? How do I find all the solutions given 1 root?

Is there another way to divide…of course! Synthetic Division

Use Synthetic Division to divide x4 – 10x2 – 2x + 4 by (x + 3) -3 1 -10 -2 4 -3 9 3 -3 1 -3 -1 1 1 remainder

Practice Problem

You Try!!

Factors vs. Roots (Zeros) Factors: What multiplies together to get the polynomial. The things in ( ) ex., (x+2), (2x-3), (x-8) Roots: What the x values equal. After setting the factor =0. Can also be called zeros, or solutions. ex., x=-2, x=3/2, x=8

Factor Theorem If remainder = 0 when we plug a #, root, into some function, then (x – #) is a factor.

Before… We could get a remainder using long division or synthetic division The last number using synthetic division is your remainder! We want a remainder of 0 to find the other roots…and we want to be able to find other roots!

Chapters 1 & 2 The Conservative Tradition in Educational Thought Determine whether (x + 2) is a factor of f(x) = 3x3 - x2 + 2x - 4 NO Answer:

You Try!! Determine whether (x - 6) is a factor of f(x) = x4 - 6x3 - 4x + 24

Can you use synthetic division when you divide by 3x-2?

Let’s Put It All Together!!

Chapters 1 & 2 The Conservative Tradition in Educational Thought If (x-1) is a factor, find the other factors of g(x) = 3x3 + 8x2 – 3x – 8 1 3 8 -3 -8 3 11 8 3 11 8 3x2 +11x +8 FACTOR using Kickback! FACTORS:

You Try!! Given that (x-10) is a factor of , find the other factors. What are the roots(zeros)?