Solving Equations by Factoring

Slides:

Advertisements

Similar presentations

Using the Zero-Product Property to Solve a Quadratic

Advertisements

Solving Equations by factoring Algebra I Mrs. Stoltzfus.

Solving Quadratic Equations using Factoring.  has the form: ax 2 + bx + c = 0 If necessary, we will need to rearrange into this form before we solve!

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

Solving Quadratic Equations by Factoring Algebra I.

Solving Equations by Factoring

3.5 Quadratic Equations OBJ:To solve a quadratic equation by factoring.

5.3.2 – Quadratic Equations, Finding Zeroes. Recall, we went over how to factor quadratics that are trinomials Example. Factor the expression x 2 + 7x.

Solving Quadratic Equations by Factoring

Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)

OBJ: To solve a quadratic equation by factoring

Copyright © Cengage Learning. All rights reserved. Factoring Polynomials and Solving Equations by Factoring 5.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Solving Quadratic Equations by Factoring.

Solving Quadratic Equations. Solving by Factoring.

1) What does x have to be for 3x = 0? 1) What does x have to be for 3(x -2) = 0 2) What does x have to be for (x–2) (x+3) = 0.

Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.

Solving Quadratic Equations Quadratic Equations: Think of other examples?

Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0

SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.

Solving Quadratic Equations by Factoring. The quadratic equation is written in the form ax 2 + bx + c = 0 To solve quadratic equations by factoring we.

Solving Quadratic Equations By Factoring Medina1.

Solving Equations by Factoring (x+3)(2x-1) (3x-1)(x-2)

Table of Contents First get all nonzero terms on one side. Quadratic Equation: Solving by factoring Example: Solve 6x 2 – 13x = 8. 6x 2 – 13x – 8 = 0 Second.

2.1 – Linear and Quadratic Equations Linear Equations.

Slide Copyright © 2009 Pearson Education, Inc. 6.9 Continued Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula.

Solving Quadratic Equations. Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)

Warm – Up # 9 Factor the following: 1.3x 2 – 2x – 5 2.4x x + 25.

Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.

Solving Quadratics Review. We must solve to get x 2 by itself 1 st !

Factoring Trinomials By Grouping Method Factoring 5/17/20121Medina.

Copyright © 2016, 2012, 2008 Pearson Education, Inc. 1 Factoring and Applications Chapter 5.

Algebra 2 cc Section 2.2 Solve quadratic equations by factoring

Objective  SWBAT solve polynomial equations. Section 9.4 “Solve Polynomial Equations in Factored Form” If ab = 0, then a = 0 or b = 0. The zero-product.

Factoring Trinomials Diamond Box Method Factoring 5/17/20121Medina.

Warm up Factor the expression.

Solve equations by factoring.

The Quadratic Formula..

Using the zero product property to solve equations

Solving Equations by Factoring

Objectives Solve quadratic equations by factoring.

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

Tuesday You need: - Calculator - Whiteboard, marker, eraser.

ZPP Zero Product Property If AB = 0 then A = 0 or B = 0.

A quadratic equation is written in the Standard Form,

5.6 – The Quadratic Formula And Ch 5 Review

The Quadratic Formula.

5.4 Factoring Quadratic Expressions

Solving Quadratic Equations by Factoring

Sec. 1.4 Quadratic Equations.

Solving Quadratics by Factoring

1B.1- Solving Quadratics:

Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48

Solving Quadratic Equations

Solving Quadratic Equations by Factoring

Review: Simplify.

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Standard Form Quadratic Equation

Solving Quadratic Equations

Warm-Up 5 minutes Factor the following expressions: 2) x2 - 3x

Factoring Using Distributive Property and Grouping

Chapter 6 Section 5.

Homework Lesson 5.3_page 296 # ALL.

Solving Quadratic Equations by Factoring

The Quadratic Formula..

The Quadratic Formula..

Objective SWBAT solve polynomial equations in factored form.

Skills Check Factoring (after the HW Check)

Presentation transcript:

Solving Equations by Factoring

The general form of a quadratic equation is: Solving Quadratic Equations The general form of a quadratic equation is: ax2 + bx + c = 0 For example : x2 – 3x + 2 = 0

We’ll use the Zero-Factor Property: Solving Quadratic Equations We’ll use the Zero-Factor Property: For any two numbers a and b, If ab = 0, then a = 0 or b = 0.

Solve: x2 – 3x + 2 = 0 (x – 1)(x – 2) = 0 So, we know that: x – 1 = 0 Example 1: Solve: x2 – 3x + 2 = 0 (x – 1)(x – 2) = 0 So, we know that: x – 1 = 0 or x – 2 = 0 x = 1 or x = 2

Solve 3x2 + 6x = 0 Solution : 3x(x + 2) = 0 3x = 0 or x + 2 = 0 x = 0 Example 2: Solve 3x2 + 6x = 0 Solution : 3x(x + 2) = 0 3x = 0 or x + 2 = 0 x = 0 or x = – 2

Solution : 5x = 6 – 6x2 6x2 + 5x – 6 = 0 (3x – 2)(2x + 3) = 0 Example 3: Solution : 5x = 6 – 6x2 Get rid of fractions! 6x2 + 5x – 6 = 0 (3x – 2)(2x + 3) = 0 3x – 2 = 0 or 2x + 3 = 0 or

Solution : x(6x2 – x – 2) = 0 x(3x – 2)(2x +1) = 0 x = 0 or 3x – 2 = 0 Example 4: Solution : x(6x2 – x – 2) = 0 Factor out GCF!! x(3x – 2)(2x +1) = 0 x = 0 or 3x – 2 = 0 or 2x + 1 = 0 x = 0,

Solving Equations by Factoring: Write the equation with 0 on right-hand side. Factor the left-hand side. Set each factor equal to 0. Solve these simpler equations.