Unit 4 Algebra Investigations Lesson 2: Factoring Polynomials and Expanding Polynomials MM1A2f. Factor expressions by greatest common factor, grouping,

Slides:

Advertisements

Similar presentations

2.6 Factor x2 + bx + c.

Advertisements

4.3 Solve x2 + bx +c = 0 by Factoring

7-5 solving quadratic equations

Lesson 9.3 Factoring Trinomials: x² + bx + c

Factoring Trinomials of the Type ax2 + bx + c

Algebra A1Mr. Brennan Chapter 10 Polynomials and Factoring Review Hamilton-Wenham Regional High SchoolDepartment of Mathematics.

Review: 6-2c Mini-Quiz 1. Factor 4x 2 – 32x Factor 3. Factor 9x x – Factor 3a a a 3x 2 + 5x + 6.

TODAY IN ALGEBRA…  Warm up: Find products of special polynomials  Learning Target: 9.4 You will solve polynomial equations in factored form  Independent.

1.3B MULTIPLYING AND DIVIDING INTEGERS I can multiply and divide integers to solve problems involving integers.

R.4 Factoring Mon Sept 8 Do Now Factor the following expressions 1) 2)

Lesson 3-2 Polynomial Inequalities in One Variable

Unit 5 Section 2.6 and 2.9 Factoring Trinomials x2 + bx + c MM1A2.f.

6.5 – Solving Equations with Quadratic Techniques.

EXPONENTS AND POLYNOMIALS College Algebra. Integral Exponents and Scientific Notation Positive and negative exponents Product rule for exponents Zero.

What are quadratic equations, and how can we solve them? Do Now: (To turn in) What do you know about quadratic equations? Have you worked with them before?

Finding Real Roots of Polynomial Equations 6-5

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.

Objectives Use the Factor Theorem to determine factors of a polynomial. Factor the sum and difference of two cubes.

Unit 5 Algebra Investigations Notes 2.13: Use Square Roots to Solve Quadratic Equations Lesson 3: Solving Polynomials MM1A3a.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 5.6 Factoring a Polynomial We have looked at factoring out a.

Quadratics Solving equations Using “Completing the Square”

Factoring. With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around Factoring = taking.

Lesson 5-11 Using Several Methods of Factoring

Bellwork Simplify the following by combining like terms.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 4e – Slide #81 A Strategy for Factoring Polynomials A Strategy for Factoring a Polynomial.

5 – 2: Solving Quadratic Equations by Factoring Objective: CA 8: Students solve and graph quadratic equations by factoring, completing the square, or using.

Unit 5 – Algebra in Context Notes 2.5: Solve Polynomial Equations in Factored Form MM1A2. Students will simplify and operate with radical expressions,

Chapter 10 Sec 3 Completing the Square. 2 of 19 Algebra 1 Chapter 10 Sections 3 & 4 Use Square Root Property Solve x x + 25 = 49. First & Last term.

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

5-4 Factoring Quadratic Expressions M11.A.1.2.1: Find the Greatest Common Factor and/or the Least Common Multiple for sets of monomials M11.D.2.1.5: Solve.

Section 10.6 Factoring Objectives: Factor a quadratic expression of the form Solve quadratic equations by factoring.

Quadratic Equations: Factoring, Square Root Methods.

Warm – up #1 Hw:pg 301 # 12-15, 21, 23, ODD (skip 45)

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

Term 2 Week 7 Warm Ups. Warm Up 12/1/14 1.Identify all the real roots of the equation: 3x x 2 – 9x Identify whether the degree is odd or.

Why we complete the square  We have learned how to factor quadratic expressions to solve.  Many quadratic equations contain expressions that cannot be.

MTH 065 Elementary Algebra II Chapter 6 – Polynomial Factorizations and Equations Section 6.2 – Equations Containing Trinomials of the Type x 2 + bx +

Warm up 1.(12x 2 + 8x – 6) – (9x 2 – 2x + 5) 2.Find the area 3.(x – 5)(-3x 2 + 6x – 8) x + 4 2x – 1.

Thurs 12/3 Lesson 5 – 5 Learning Objective: To write equations given roots Hw: Pg. 315#23 – 29 odd, 37 – 41 odd, 42, 45.

Section 5-5: Factoring Using Special Patterns Goal: Factor Using Special Patterns.

Sect. 5.7 Summary of Factoring Techniques  General Factoring Strategy: Z: (if needed) Arrange in Descending Order of Exponents A: (if needed) Factor out.

SAT Problem of the Day. 5.3 Factoring Quadratic Expressions 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring.

Do Now: Solve x2 – 20x + 51 = 0 3x2 – 5x – 2 = 0 Today’s Agenda

Factoring Polynomials.

Section 5-3: Factoring x 2 + bx + c Goal: Factor trinomials of the form x 2 + bx + c.

Factoring Trinomials of the Type x 2 + bx + c ALGEBRA 1 LESSON Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 2.Factors of 12: 1, 2, 3, 4, 6, 12 3.Factors.

Solving Radical Equations and Inequalities Section 5.8.

Algebra 1 Section 4.3 Graph Linear Equations by using Intercepts A linear equation (the graph is a line) takes the form Ax + By = C. Which are linear equations?

Completing the Square, Quadratic Formula

Use Inverse Matrices to Solve Linear Systems

Notes Over 10.8 Methods of Factoring Binomial Trinomial

Objectives Factor out the greatest common factor of a polynomial.

Solve Polynomial Equations in Factored Form

(12x2 + 8x – 6) – (9x2 – 2x + 5) Find the area (x – 5)(-3x2 + 6x – 8)

Lesson 0 – 4 & 0 – 5 Algebraic Expressions & Linear Equations

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

2.6 Factor x2 + bx + c provided ________ = b and ______ = c

Finding Real Roots of Polynomial Equations 3-5

Factoring a Quadratic Expression

5.5 Completing the Square.

Factor Special Products

Factoring ax2 + bx + c Objective:

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

2.6 Factor x2 + bx + c provided ________ = b and ______ = c

Factoring x2 + bx + c Objective:

(5x – 2)(x + 3) = 0 5x – 2 = 0 x + 3 = 0 x = -3 x = 2/5

Review: 6.5c Mini-Quiz 1. Solve: 4x2 – 40 = –27x.

Algebra Section 8-3 Notes

Unit 2 Algebra Investigations

Presentation transcript:

Unit 4 Algebra Investigations Lesson 2: Factoring Polynomials and Expanding Polynomials MM1A2f. Factor expressions by greatest common factor, grouping, trial & error, and special products. MM1A3c. Use a variety of techniques, including technology, tables, & graphs to solve equations resulting from investigation of x ² + bx+c = 0 Notes 2.6: Factor x 2 + bx + c

Factoring x 2 + bx + c Algebra: x 2 + bx + c = (x + p)(x + q) provided ______ = b and ____ = c. Example: x 2 + 6x + 5 = (_____) (_____) because ________ = 6 and ______ = 5

Factoring Tricks The SIGNS of the terms in your trinomial will give you a clue as to it’s factored form!! x 2 + bx + c When b and c are positive x 2 + bx + c (x + _)(x + _) When b is negative and c is positive x 2 - bx + c (x - _)(x - _) When b is positive and c is negative x 2 + bx - c (x + Larger )(x – smaller ) When b is negative and c is negative x 2 - bx - c ( x – larger )(x + smaller )

Preview Practice Examples:

(Ex 1) Factor when b and c are positive. Factor: x x + 16 Factor: y ² + 6y + 5

(Ex 2) Factor when b is negative and c is positive. Factor: a 2 – 5a + 6 Factor: w ² - 10w + 9

(Ex 3) Factor when b is positive and c is negative. Factor: y 2 + 3y – 10 Factor: x ² + 6x - 7

Ex: 4 Solve polynomial equation x ² - 4x = 21

Checkpoint: Factor the trinomial. 1. x 2 + 7x x 2 + 9x x 2 – 12x + 27

Checkpoint: Factor the trinomial. 4. x 2 – 9x y 2 + 4y – z 2 + 2z – 24

Assignment Pg. 83 # 1-9, 11 – 18 (odd)