6.4: Solving Polynomial Equations. Solving by Graphing 1. 3x 3 – 6x 2 – 9x =0 2. 6x 2 = 48x.

Slides:

Advertisements

Similar presentations

6.4 Solving Polynomial Equations

Advertisements

EXAMPLE 6 Solve a multi-step problem TERRARIUM

Chapter 6 – Polynomials and Polynomial Functions

Find a common monomial factor

Do now: These cuboids are all made from 1 cm cubes

EXAMPLE 6 Solve a polynomial equation City Park

Essential Question: Describe two methods for solving polynomial equations that have a degree greater than two.

Factoring and Solving Polynomial Equations Section 6.4

Multiplying Polynomials

Volume word problems Part 2.

Daily 10. Day 1 1. Given the dimensions of the large and small rectangles, find the area of the shaded region: A. 7x 2 + 6x - 2 B. 7x x + 10 C.

2.9 Warm Up 1. Solve 2x2 + 11x = , –7 ANSWER 2

Warm-up Find the quotient Section 6-4: Solving Polynomial Equations by Factoring Goal 1.03: Operate with algebraic expressions (polynomial,

Solving systems of equations with 2 variables

5.4 Do Now: Factor completely.

Factoring Special Products

2.4 Factor and Solve Polynomial Equations p. 111 Name two special factoring patterns for cubes. Name three ways to factor a polynomial. What is the difference.

Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression

Factor and Solve Polynomial Equations 2.3 (GREEN book) Polynomial Review WS: due TOMORROW.

Warm-Up Exercises Multiply the polynomial. 1.(x + 2)(x + 3) ANSWER x 2 + 5x + 6 ANSWER 4x 2 – 1 2.(2x – 1)(2x + 1) 3. (x – 7) 2 ANSWER x 2 – 14x + 49.

Section 6.4 Solving Polynomial Equations Obj: to solve polynomial equations.

4.8 Polynomial Word Problems. a) Define the variable, b) Write the equation, and c) Solve the problem. 1) The sum of a number and its square is 42. Find.

7.3.1 Products and Factors of Polynomials Products and Factors of Polynomials Objectives: Multiply and factor polynomials Use the Factor Theorem.

6.4 Solving Polynomial Equations. One of the topics in this section is finding the cube or cube root of a number. A cubed number is the solution when.

GOAL: FACTOR CUBIC POLYNOMIALS AND SOLVE CUBIC EQUATIONS Section 6-5: Factoring Cubic Polynomials.

Perfect square trinomial x x + 25 = ( x + 5) 2

Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +

Algebra 2 Ch.6 Notes Page 43 P Solving Polynomial Equations.

Factor and Solve Polynomial Equations 2.3 (GREEN book)

Section 5.3 – Solving Polynomial Equations Students will be able to: Solve polynomial equations by factoring Solve polynomial equations by graphing Lesson.

6-4 Solving Polynomial Equations. Objectives Solving Equations by Graphing Solving Equations by Factoring.

Holt McDougal Algebra 2 Multiplying Polynomials How do we multiply polynomials? How do we use binomial expansion to expand binomial expressions that are.

Factoring Polynomial Expressions Previously, you learned how to factor the following types of quadratic expressions. TypeExample General trinomial Perfect.

Lesson 6.4 Factoring and Solving Polynomial Equations.

5.5B – Synthetic Division. If I tell you that (x – 1) is a factor of the equation above, what does that tell you? x = 1 is a solution.

CHAPTER 8 REVIEW EXAM You may need paper and pencil to simplify and/or solve some of the problems in this review.

Notes Over 3.4Volume The volume of a box is the number of cubic units it can hold. Rectangular box: Cube: Sphere:

Remainder Theorem Section 6-3b. Remainder Theorem.

Chapter 5 Section 4. EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x.

Squared and Cubed Conversion Factors

Objective: I can factor a perfect cube and solve an equation with a perfect cube Warm Up 1.Determine if x – 2 is a factor of x³ - 6x² Use long division.

Go Back > Question 1 8x 3 ? A cube has side length 2x. What is its volume? 2a.

Warm-Up Exercises EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x –

6.4: Factoring and Solving Polynomial Equations Objectives: Students will be able to… Factor the sum and difference of 2 cubes Factor by grouping Solve.

Warm up Factor the expression.

Section 10.8 Factoring Using the Distributive Property

Factor Polynomials Completely

Solving Equations & Inequalities

Objectives Factor the sum and difference of two cubes.

Warm up Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Do Now: Factor the polynomial. (5.4 worksheet B)

Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)

2.2 Multiply Polynomials Multiply a monomial and a polynomial

Chapter 4 Review Polynomials.

2.2 Multiply Polynomials Multiply a monomial and a polynomial

Warm Up - September 27, 2017 Classify each polynomial by degree and by number of terms. 1. 5x x2 + 4x - 2 Write each polynomial in standard form.

Factor and Solve Polynomial Equations

Opener Perform the indicated operation.

7.3 Products and Factors of Polynomials

10/10/ Bell Work Write and answer the following questions.

Half Test Review! Day 6.

Factorization by Using Identities of Sum and Difference of Two Cubes

Exponents and Exponential Form

Problem of the Day Factor the following: x2 – 16 x2 + 7x + 12

Warm Up Factor the following: a) b).

Factoring Introduction

Factoring Polynomials, Special Cases

Presentation transcript:

6.4: Solving Polynomial Equations

Solving by Graphing 1. 3x 3 – 6x 2 – 9x =0 2. 6x 2 = 48x

3. 2x 3 + 5x 2 = 7x 4. 12x 3 = 60x x

The volume V of a container is modeled by the function V(x) = x 3 – 3x 2 – 4x. Let x, x + 1, and x – 4 represent the width, the length, and the height respectively. The container has a volume of 70ft 3. Find the container’s dimensions.

Sum of Cubes (a 3 + b 3 ) = (a + b)(a 2 – ab + b 2 ) Difference of Cubes (a 3 – b 3 ) = (a – b)(a 2 + ab + b 2 )

Factor each expression. 1. x x 3 – 1

Solve each equation x = 0 2. x 3 – 27 = 0

Factor each expression. 1. x 4 – 8x x 4 – 6x x 4 – 7x

Solve each equation. 1. x 4 – 10x = 0 2. x 4 – 12x 2 – 64 = 0 3. x 4 + 7x 2 – 18 = 0

Solve each equation. 1. x 3 + 2x 2 + x +2 = x 3 + 3x x + 21 = x 3 – 6x 2 + x – 3 = 0

S olve each equation x 3 – 192 = x x 2 = x 5 – 5x 3 + 4x = x 4 – 14x x 2 = 0