Dividing Polynomials (Long Division)

Slides:



Advertisements
Similar presentations
Divide each term of the numerator by 6y
Advertisements

Simplifying Fractions Multiplying & dividing Fractions.
7/14/ :41 AM6.4 - Dividing Polynomials (Long Division)1 Polynomial Division SECTION 6.4 LONG DIVISION and Synthetic Division.
EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial function.
Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression following the division.
EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. – – 8 5 – 6 15 – 21 2 – 5 7 – 16 2x 3 + x 2.
6.8 Synthetic Division. Polynomial Division, Factors, and Remainders In this section, we will look at two methods to divide polynomials: long division.
Vocabulary  Rational Expression – a ratio of 2 polynomial expressions.  Operations with rational numbers and rational expressions are similar.  Just.
Concepts 1, 2, Division of Polynomials Division by a Monomial Example:
Warm Up Divide using long division ÷ ÷
3.7Divide Polynomials Example 1 Divide a polynomial by a monomial Divide 10x 3  25x x by 5x. Solution Method 1: Write the division as a fraction.
5.4 – Apply the Remainder and Factor Theorems Divide 247 / / 8.
Dividing Polynomials MATH 017 Intermediate Algebra S. Rook.
Section 3-3 Dividing Polynomials Objectives: Use Long Division and Synthetic Division to divide polynomials.
5-3 Dividing Polynomials Objectives Students will be able to: 1) Divide polynomials using long division 2) Divide polynomials using synthetic division.
5.6 Dividing Polynomials.
My own word  I think synthetic division is a short cut for long division  Long division is the same as regular long division just doing it with polynomials.
4.2 – Synthetic Division. Just as with real numbers, we can use division in regards to polynomials Two different methods; we will focus on what is known.
5. Divide 4723 by 5. Long Division: Steps in Dividing Whole Numbers Example: 4716  5 STEPS 1. The dividend is The divisor is 5. Write.
6.3 Dividing Polynomials 1. When dividing by a monomial: Divide each term by the denominator separately 2.
Objective Use long division and synthetic division to divide polynomials.
In this case, the division is exact and Dividend = Divisor x Quotient
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,
Essential Questions How do we use long division and synthetic division to divide polynomials?
Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.
5.3 Dividing Polynomials Objectives: 1.Divide polynomials using long division 2.Divide polynomials using synthetic division.
Dividing Polynomials. To divide a polynomial by a monomial, divide each term by the monomial.
5.5a – Long Division.
Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:
Warm up Objective: To divide polynomials Lesson 6-7 Polynomial Long Division.
Moon 11/23 Lesson 5 – 4 Learning Objective: To divide polynomials by long division Hw: Pg.
Divide Polynomials using Long Division and Synthetic Division.
9.4 Polynomial Division, Factors, and Remainders ©2001 by R. Villar All Rights Reserved.
SOLUTION Divide a polynomial by a monomial EXAMPLE 1 Divide 4x 3 + 8x x by 2x. Method 1 : Write the division as a fraction. Write as fraction. Divide.
Notes Over 6.5 Using Polynomial Long Division
Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.
Aims: To recap the remainder and factor theorems. To be able to divide a polynomial by another polynomial using your preferred method To understand terminology,
Dividing Polynomials/Long and Synthetic Division Section 6.3.
Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.
MAIN IDEAS DIVIDE POLYNOMIALS USING LONG DIVISION. 6.3 Dividing Polynomials.
Chapter Dividing polynomials. Objectives  Use long division and synthetic division to divide polynomials.
8.2: Multiplying and Factoring. Warm-up:  Greatest Common Factor (GCF)  The greatest factor that divides evenly into each term of an expression  Find.
11-3 Dividing Polynomials Hubarth Algebra. Divide (18x 3 + 9x 2 – 15x) by 3x 2. (18x 3 + 9x 2 – 15x)3x23x2 ÷= 1 3 x 2 = + – 18x 3 3x 2 9x23x29x23x2 15x.
Objective Use long division and synthetic division to divide polynomials.
Divide using long division.
Warm Up Divide using long division ÷ Divide.
Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.
Warm Up Divide using long division ÷ ÷
Dividing Polynomials Section 4.3.
5.2 Dividing Polynomials.
8.1 Multiplying and Dividing Rational Expressions
1a. Divide using long division. (9x3 – 48x2 + 13x + 3) ÷ (x – 5)
Remainder Theorem Section 5.5 Part 1.
5-3 Dividing Polynomials
Section 6.3 Dividing Polynomials
Objective Use long division and synthetic division to divide polynomials.
Without a calculator, simplify the expressions:
Remainder and Factor Theorem
Synthetic Division Much easier shortcut to Polynomial division.
Division of a Polynomial by a Monomial
Solving Special Cases.
Dividing Polynomials (Long Division)
Section 6.3 – Polynomial Division
Dividing Polynomials (Long Division)
Dividing Polynomials The long way.
Dividing Polynomials (Long Division)
3.7 Divide Polynomials - + Divide a polynomial by a monomial = =
Division of Polynomials
Warm Up Honors Algebra 2 11/3/17
Divide 9 × by 3 ×
Presentation transcript:

Dividing Polynomials (Long Division) 5/8/2019 10:50 AM Dividing Polynomials (Long Division)

Polynomial long division is a method for dividing a polynomial by another polynomials of a lower degree. It is very similar to dividing numbers.

Dividing Polynomials (Long Division) Example 1 Divide (x3 – 28x – 48) ÷ (x + 4) 5/8/2019 10:50 AM5/8/2019 10:50 AM Dividing Polynomials (Long Division) 4 4

Dividing Polynomials (Long Division) Example 2 Rewrite in long division form... Divide (2x2 + 3x – 4) ÷ (x – 2) 5/8/2019 10:50 AM5/8/2019 10:50 AM Dividing Polynomials (Long Division) 5 5

Dividing Polynomials (Long Division) Example 3 Divide (12x4 - 5x2 – 3) ÷ (3x2 + 1) 5/8/2019 10:50 AM5/8/2019 10:50 AM Dividing Polynomials (Long Division) 6 6

Dividing Polynomials (Long Division) Example 4 Divide (x3 – 6) ÷ (x – 1) 5/8/2019 10:50 AM5/8/2019 10:50 AM Dividing Polynomials (Long Division) 7 7

Problem 1A divide A B C Partner activity 1 D

Problem 2A divide A B C Partner activity 1 D

Problem 3A divide A B C Partner activity 2 D

Problem 4A divide A B C Partner activity 2 D

Problem 1B divide A B C Perhaps….additional partner activity if things go faster than planned. D

Problem 2B divide A B C Perhaps….additional partner activity if things go faster than planned. D

Problem 3B divide A B C D

Problem 4B divide A B C D