Factor and Solve Polynomial Equations 2.3 (GREEN book)

Slides:

Advertisements

Similar presentations

Find a common monomial factor

Advertisements

Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7)

Objectives: 1. Solve equations by: A. Factoring B. Square Root of Both Sides C. Completing the Square D. Quadratic Formula 2. Solve equations in quadratic.

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

Factoring and Solving Polynomial Equations Section 6.4

POLYPACK REVIEW

X-box Factoring. X- Box 3-9 Product Sum X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 6 Factoring.

Essential Question: How do you factor a trinomial and how is it used to solve a quadratic equation? Students will write a summary that describes factoring.

5.4 Do Now: Factor completely.

Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Introduction to Factoring Common Factors Factoring by Grouping 6.1.

Factoring Special Products

Factoring and Solving Polynomial Equations Chapter 6.4.

Objectives I will use the distributive property to factor a polynomial.

Multiplying Polynomials. Multiply monomial by polynomial.

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.

9-4 Factoring Trinomials ax2 + bx + c

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

EXAMPLE 3 Factor by grouping Factor the polynomial x 3 – 3x 2 – 16x + 48 completely. x 3 – 3x 2 – 16x + 48 Factor by grouping. = (x 2 – 16)(x – 3) Distributive.

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

5.4 Factor and Solve Polynomial Equations. Find a Common Monomial Factor Monomial: means one term. (ex) x (ex) x 2 (ex) 4x 3 Factor the Polynomial completely.

HA2 Ch. 5 Review PolynomialsAnd Polynomial Functions.

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.

WARM UP Find the product. 1.) (m – 8)(m – 9) 2.) (z + 6)(z – 10) 3.) (y + 20)(y – 20)

Factoring Polynomials Section 2.4 Standards Addressed: A , A , CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.5.

5.4 Factor and Solve Polynomial Functions SWBAT Factor and Solve Polynomial Functions.

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 +

Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring.

Mark Dugopolski Elementary Algebra Edition 3 Chapter 5 Factoring Copyright © 2000 by the McGraw-Hill Companies, Inc.

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

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

Quiz Simplify: 2. Simplify: Simplify (special pattern):

5-4 Factoring Quadratic Expressions Big Idea: -Factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference.

Factor and Solve Polynomial Equations Homework Questions?

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

MTH 065 Elementary Algebra II Chapter 6 – Polynomial Factorizations and Equations Section 6.6 – Factoring: A General Strategy.

Lesson 6.4 Factoring and Solving Polynomial Equations.

Questions about 2.8 HW…. 2.9 Factor Polynomials Completely Test: Friday Midterm: March 11.

8.5: FACTORING AX 2 + BX + C where A=1. Factoring: A process used to break down any polynomial into monomials.

X-box Factoring.

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.

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

SECTION 2.4 Factoring polynomials. Do-Now  Factor the following polynomials.  x 2 + 5x + 6  4x 2 – 1  Solve the following equations.  2x 2 – 28x.

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 –

Bellwork Multiply (x+2)(x+3) 2) Put in Vertex Form 3)

Warm up Factor the expression.

Section 10.8 Factoring Using the Distributive Property

Polynomials & Factoring

Section 6.4: Factoring Polynomials

Polynomial Equations and Factoring

Factoring Polynomials

4.5 & 4.6 Factoring Polynomials & Solving by Factoring

Do Now: Factor the polynomial.

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

Factoring Trinomials of the form

POLYPACK REVIEW

Chapter 4 Review Polynomials.

Factoring Quadratics.

Review of Factoring; Quadratic Equations and Rational

Identifying Terms, Factors, and Coefficients (3.1.1)

Polynomials and Polynomial Functions

The Quadratic Formula.

Lesson 9.8 Factor Polynomials Completely

3.4 Solve by Factoring (Part 1)

Get Started!! x  , y  ______.

Do Now 3/4/19 Take out your HW from last night.

Presentation transcript:

Factor and Solve Polynomial Equations 2.3 (GREEN book)

Vocabulary A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.

I. GCF - Always!! II. 2 Terms A. Difference of Squares a 2 – b 2 = _____________________________ B. Sum of Cubes a 3 + b 3 = _____________________________ C. Difference of Cubes a 3 – b 3 = ____________________________ III. 3 Terms A. Trinomial Square a. a 2 + 2ab + b 2 = __________________________ b. a 2 – 2ab + b 2 = __________________________ B. Plain Trinomial a. x 2 + bx + c ___________________ b. ax 2 + bx + c ___________________________ IV. 4 Terms - Grouping Factoring Quadratic Equations

Vocabulary For some polynomials you can factor by grouping pairs of terms that have a common monomial factor.

Example 1: Factor the polynomial completely 1. 4x 4 – 108x 2. 2b a 3

Example 2: Factor the polynomial x 3 + 2x 2 – x – 2 completely.

Example 3: Factor completely: 1. 3x x x g

Example 4: Find the real-number solutions of the equation x 4 – 7x 2 = -12

Example 5. The dimensions (in inches) of a jewelry box are: length 4x, width (x – 1), and height (x – 2). If the volume of the box is 24 cubic inches, find the dimensions of the box.