Polynomials By C. D.Toliver. Polynomials An algebraic expression with one or more terms –Monomials...

PolynomialsPolynomialsBy C. D.ToliverBy C. D.Toliver

PolynomialsPolynomials• An algebraic expression with one or

more terms– Monomials have one term, 3x– Binomials have two terms, 3x

+ 4– Trinomials have three terms, x2

+ 3x + 4

Review:Review: Collecting Like Terms Collecting Like Terms

• You simplify polynomial expressions by collecting like terms

• Like terms have the same variable and the same exponent.2a, 5a, -7a are like terms

2a, 5b, 6c are not like terms a3, a2, a are not like terms• Constants are also like terms 2, 0.5, ¼ are like terms

ReviewReviewCollecting Like TermsCollecting Like Terms

Example 1. Simplify3x2 + 5x – 2x2 + 3x + 73x2 + 5x – 2x2 + 3x + 71x2 + 8x + 7

Example 2. Simplify(5a + 7b + 6) + (- 8a - 9b + 5)5a + 7b + 6 + - 8a + - 9b + + 55a + 7b + 6 - 8a - 9b + 5-3a – 2b + 11

Example 4. Simplify(5a + 7b + 6) – (8a - 6b + 5)5a + 7b + 6 - 8a - -6b -+55a + 7b + 6 - 8a + 6b - 5-3a + 13b + 1

Review:Review: Distributive Property Distributive Property

• We also learned that parenthesis mean to multiply.

• We use the distributive property to multiply polynomials

• The distributive property says: a(b+c) = a(b) + a(c)

Example 1 Multiply3(x+y) 3(x) + 3(y)3x +3y

Example 2. Multiply4(2x – 3)4(2x) + 4(-3)8x -12

Review:Review: Distribute and Collect Distribute and Collect

• For more complex expressions you may need to distribute and collect like terms.

• Distribute first• Then collect

Example 1. Distribute and Collect6(x + 5) - 2(2x – 8)6(x) +6(5) -2(2x) -2(-8) Distribute6x + 30 – 4x + 16 Collect2x + 46

Example 2. Distribute and Collect3(2x - 4) + 7(x – 2) 3(2x) + 3(-4) +7(x) + 7(-2)Distribute6x - 12 + 7x - 14 Collect13x - 26

Example 3. Distribute and Collect5(y - 3) + 4(6 - 2y)5(y) +5(-3) +4(6) +4(-2y)Distribute5y - 15 +24 – 8y Collect-3y + 9

Multiply PolynomialsMultiply Polynomials• In the previous examples, we were

multiplying polynomials by a monomial, e.g., 3 (x+2)

• 3 is a monomial• x+2 is a polynomial• What happens when you multiply two

polynomials, e.g., (x + 4)(x+2)?

Multiply PolynomialsMultiply Polynomials• We will look at three different

methods to multiply polynomials• You may prefer one method over

another• Today we will practice all three

methods

Multiply PolynomialsMultiply PolynomialsDistributive MethodDistributive Method

Example 1. Multiply(x + 4)(x + 2)x(x+2) + 4(x+2) Distributex(x) + x(2) + 4(x) +4(2) Distributex2 + 2x + 4x + 8 Collectx2 + 6x + 8

Multiply PolynomialsMultiply PolynomialsVertical MethodVertical Method

Example 1. Multiply(x + 4)(x + 2) Rewrite vertically

X + 4X + 22x + 8 Multiply

x2 + 4x Multiply x2 + 6x + 8 Combine

Multiply PolynomialsMultiply PolynomialsBox MethodBox Method

Example 1. Multiply(x + 4)(x + 2)=x2 + 6x + 8

Example 2. Multiply(x - 3)(x + 5)x(x+5) - 3(x+5) Distributex(x) + x(5) - 3(x) -3(5) Distributex2 + 5x - 3x - 15 Collectx2 + 2x - 15

Example 2. Multiply(x - 3)(x + 5) Rewrite vertically

X - 3X + 5

5x - 15 Multiply x2 - 3x Multiply x2 + 2x - 15 Combine

Example 2. Multiply(x - 3)(x + 5)=x2 + 2x - 15

x2 -3x

5x -15

Example 3. Multiply(2x + 1)(x - 4)2x(x-4) + 1(x-4) Distribute2x(x)+2x(-4)+1(x)+1(-4) Distribute2x2 - 8x + 1x -4 Collect2x2 - 7x - 4

Example 3. Multiply(2x + 1)(x - 4) Rewrite vertically

2x + 1x - 4

-8x - 4 Multiply 2x2 + 1x Multiply 2x2 - 7x - 4 Combine

Example 3. Multiply(2x + 1)(x - 4)=2x2 - 7x - 4

2x2 1x

-8x -4

Example 4. Multiply(2x + 3)(3x - 4)2x(3x-4)+3(3x-4) Distribute2x(3x)+2x(-4)+3(3x)+3(-4)Distribute6x2 - 8x + 9x - 12 Collect6x2 + 1x - 12

Example 4. Multiply(2x + 3)(3x - 4) Rewrite vertically

2X + 3 3X - 4 -8x - 12 Multiply

6x2 + 9x Multiply 6x2 + 1x - 12 Combine

Example 4. Multiply(2x + 3)(3x - 4)=6x2 + 1x - 12

6x2 9x

-8x -12

Polynomials By C. D.Toliver. Polynomials An algebraic expression with one or more terms –Monomials...

Documents

Transcript of Polynomials By C. D.Toliver. Polynomials An algebraic expression with one or more terms –Monomials...

6.2 Graphs of Polynomials. The Degree of Polynomials The degree of a polynomial is the value of the largest exponent. y = 5x 4 + 3x 2 – 7 Degree = 4 y.

Factoring Polynomials Factoring Polynomials Factoring Polynomials.

Identify terms and coefficients. Know the vocabulary for polynomials. Add like terms. Add and subtract polynomials. Evaluate polynomials. 5.4 2 3 4 5 2.

5.3: Add, Subtract, & Multiply Polynomials Objectives: 1.To define a polynomial and related terms 2.To find the sum, difference, and product of polynomials.

Unit 4 Operations & Rules. Combine Like Terms 1) 3x – 6 + 2x – 8 2) 3x – 7 + 12x + 10 Exponent Rules 3) What is 2x 3x? 5x – 14 15x + 3 6x 2 Warm up.

Lesson 6 - WordPress.com · MPM1D – Principles of Mathematics Unit 2 ... Lesson Six Concepts ¾ Introduction to polynomials ¾ Like terms ¾ Addition and subtraction of polynomials

Let’s Get Together! Combining Like Terms in Polynomials

Painlevé equations and orthogonal polynomialsare in terms ofparabolic cylinder functions. Walter Van Assche Painlev e equations and orthogonal polynomials Orthogonal polynomials on

Name Adding and Subtracting Polynomials - Mr. Beals …mrbealsquest.weebly.com/uploads/9/6/0/0/9600167/alg2-2.pdf · Name Adding and Subtracting Polynomials + 7x-f)-(x2-3x + 4) =

8-1 Adding Polynomials - Manasquan Public Schools · 2016-05-04 · Adding and Subtracting Polynomials . ... 5X+9 4x2+ 7x+3 8x4-2x3+3x Constant Linear Quadratic ... 8-1 Adding and

Classifying Polynomials · Classifying Polynomials Learning Intention(s): Identify different types of polynomials Be able to identify and combine like terms Use distributive property

Kinds Of Polynomials According To Terms ezdock

UNIT 3 POLYNOMIALS 5-1 Graphing Polynomials. Key Terms for Classifying Polynomials Define: Polynomial – is a monomial or a sum/difference of monomials.

X + 5 4x +20x R + 3 3x - 16 3x - +15 -31 - - -. Tues 11/24 Lesson 5 – 4 Learning Objective: To divide polynomials by synthetic division Hw: Pg. 308 #21-29.

POLYNOMIALS. MULTIPLYING POLYNOMIALS REVIEW Polynomials:

Unit 6 Factoring Polynomials Greatest Common Factor Factoring by Grouping (Four Terms) AC Method (3 Terms) Difference of Two Squares (2 Terms)

Lesson Summary - Pre-algebra€¦ · Pre-Algebra Essential Question: How do we add and subtract polynomials? Lesson Summary Adding Polynomials 1) Combine like terms (like terms have

Section 5.1 Modeling Polynomials · Grade 9: Unit 5- Polynomials Section 5.1 Modeling Polynomials Polynomial: an algebraic expression that contains one term or a sum of terms. The

Adding and Substracting Polynomials · Adding and Subtracting Polynomials What are like terms?Like terms have the same variables with exactly the same exponents Which of the following

5.4 SUBTRACTING POLYNOMIALS - HOMEWORK · Subtracting Polynomials (3x² – 4x) – (2x² – 6x) 2. ADD ZERO PAIRS if necessary 1. TAKE AWAY the appropriate number of tiles • You