Get out your homework, but keep it at your desk..

Slides:

Advertisements

Similar presentations

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Advertisements

5.5 Apply the Remainder and Factor Theorem

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

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.)

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

PRE-AP PRE-CALCULUS CHAPTER 2, SECTION 4 Real Zeros of Polynomial Functions

HW: Pg #13-61 eoo.

Section 2.4 Dividing Polynomials; Remainder and Factor Theorems.

Long Division Algorithm and Synthetic Division!!!

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

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.

Copyright © 2009 Pearson Education, Inc. CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions.

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.

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.

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,

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.

6.5 The Remainder and Factor Theorems

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.

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.

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

Warm Up 1.What is the absolute minimum of f(x) = 2x 4 – 17x x 2 – 7x – 15 2.A ball is thrown into the air. It’s height above the ground in feet is.

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

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.

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.

5.3 Dividing Polynomials Objectives: 1.Divide polynomials using long division 2.Divide polynomials using synthetic division.

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

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.

Warm UpMar. 5 th 1.What is the absolute minimum of f(x) = 2x 4 – 17x x 2 – 7x – 15 2.A ball is thrown into the air. It’s height above the ground.

2.5 – Apply the remainder and factor theorems

5.5 – Dividing Polynomials Divide 247 / / 8.

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.

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

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

A polynomial function is a function of the form f (x) = a n x n + a n – 1 x n – 1 +· · ·+ a 1 x + a 0 Where a n  0 and the exponents are all whole numbers.

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

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.

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?

Division of a Polynomial

Pre-Calculus Section 2.3 Synthetic Division

Remainder and Factor Theorems

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

2.3 Notes: Polynomial and Synthetic Division

Dividing Polynomials Algebra

Multiplying and Dividing Polynomials

Apply the Remainder and Factor Theorems

Polynomial Long Division

Real Zeros of Polynomial Functions

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.

Multiplying and Dividing Polynomials

Divide using long division

5.5 Apply the Remainder and Factor Theorems

3.2 The Remainder Theorem.

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

Dividing Polynomials (SYNTHETIC Division)

Presentation transcript:

Get out your homework, but keep it at your desk.

Dividing Polynomials get out a coin for the traffic signal

Review of long division…

Remember all exponents must be accounted for and have a place holder when dividing…

Review of synthetic division… Remember the divisor must be in the form (x – k) to use this method. In other words, the leading coefficient and the exponent on x must be 1.

The Remainder theorem… Given f(x) = x 4 – 10x 2 – 2x + 4 Find f(-3).

Factor Theorem… What makes a number a “factor” of another number? For example…why is 3 a factor of 12? (x – k) is a factor of f(x) if and only if the remainder is 0 … f(k) = 0.

Show that x = -4 is a solution to x 3 – 28x – 48 = 0. Use this to completely factor f(x) = x 3 – 28x – 48 Show that x = -2 is a solution to x 3 + 2x 2 – 3x – 6 = 0. Use this to completely factor f(x) = x 3 + 2x 2 – 3x – 6

Use the graph to guess possible linear factors of f(x). Then completely factor f(x). F(x) = 5x 3 – 12x 2 – 23x + 42