Factoring Quadratic Equations

Slides:

Advertisements

Similar presentations

Factorising polynomials

Advertisements

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.

Algebra 2 Bell-work 10/14/2014 Multiple Choice: Which set of ordered pairs is a solution to the system? 4x + 2y = 4 6x + 2y = 8 A. (7,5)B. (2,4)C. (2,-2)D.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by FACTORING

 Radical Equations Quadratic Formula. Remember: 1. Simplify x 2 – x = 6 is therefore a 2 nd degree equation Aim: Use the quadratic formula in order to.

Quadratic Equations By Dr. Carol A. Marinas. Solving Equations In the previous section, we solved LINEAR equations. This means that the highest exponent.

The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

1 Aims Introduce Quadratic Formulae. Objectives Identify how to solve quadratic equation’s using a quadratic equation.

Quadratics Solving equations Using “Completing the Square”

Objective 9.1 Students will be able to: classify polynomials and write polynomials in standard form; evaluate polynomial expressions; add and subtract.

Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2.

Algebra 3 Lesson 2.1 Objective: SSBAT multiply polynomial expressions. Standards: M11.D

 We visited this idea earlier, and will build on it now  How would we factor 3x x + 6? ◦ Recall, to factor x 2 + 2x + 3, we put one ‘x’ in each.

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

Chapter 5.2 Solving Quadratic Equations by Factoring.

Solving Quadratic Equations Quadratic Equations: Think of other examples?

By Kendal Agbanlog 6.1-Measurement Formulas and Monomials 6.2-Multiplying and Dividing Monomials 6.3-Adding and Subtracting Polynomials 6.4-Multiplying.

WHAT IS A “SOLUTION”? Sect P.5 solving Equations.

Solving a quadratic by factorisation 6x 2 + 7x – 3 = 0 ac = -18 b = 7 Factors are: , , +2 -9, , , Correct pair adding to.

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.

13.1 Introduction to Quadratic Equations

2.4 part 1 - Basic Factoring I can... - Factor using GCF -Factor a difference of two perfect squares -Factor basic trinomials.

Dividing polynomials This PowerPoint presentation demonstrates two different methods of polynomial division. Click here to see algebraic long division.

Sometimes, a quadratic equation cannot be factored Example: x 2 + 7x + 3 = 0 There is not a pair of numbers that multiply to give us 3, that will also.

DO NOW 11/12/14 Homework in the basket please Multiply the following polynomials 1. (3x + 1)(3x – 1) 1. (2z – 7)(z + 4) 1. (4a + 2)(6a2 – a + 2) 1. (7r.

Introduction This chapter focuses on basic manipulation of Algebra It also goes over rules of Surds and Indices It is essential that you understand this.

11/06/ Factorizing Quadratic Equations. 11/06/ x 2 ± bx ± c x 2 ± bx ± c If this is positive, both signs are the same. The numbers ADD to.

Factoring Day 1 I can factor a quadratic expression. x 2 + 3x + 2 Rewrite as (x + 1)(x + 2)

Elimination Method - Systems. Elimination Method  With the elimination method, you create like terms that add to zero.

XEI: Expressions, equations, and inequalities

Discriminant and Quadratic

Solving Quadratic Equation by Graphing

GCSE Revision 101 Maths Quadratics © Daniel Holloway.

The Quadratic Formula..

Quadratic Formula Solving for X Solving for quadratic equations.

The student will be able to:

Objective: SSBAT multiply polynomial expressions.

Quadratic Equations.

Factoring Quadratic Equations when a = 1

Solving quadratic equations

Solving Quadratic Equation and Graphing

Homework Check.

3.2 Solve Linear Systems Algebraically

Solve Quadratic Systems

Solving a Quadratic Equation by Graphing

Factoring Quadratic Equations

SOLVING QUADRATIC EQUATIONS USING THE FORMULA

The Quadratic Formula.

Factoring Quadratic Functions if a ≠ 1 (Section 3.5)

Solving Quadratic Equations

6.4 Factoring and Solving Polynomial Equations

Solving Quadratic Equation

Factorising quadratics

Solving Quadratic Equations by Factoring

The student will be able to:

5.4 Completing the Square.

The Quadratic Formula..

A, b and c can be any numbers

Solving Quadratic Equations by FACTORING

The Quadratic Formula..

Solving Systems by ELIMINATION

There is a pattern for factoring trinomials of this form, when c

Factoring Polynomials

A, b and c can be any numbers

A, b and c can be any numbers

Presentation transcript:

Factoring Quadratic Equations

What are Quadratic Equations? A quadratic equation is an equation which: y = x2 y = x2 + 2 y = x2 + x – 4 y = x2 + 2x – 3 The highest exponent is 2 All of these equations contain a x2 term therefore they are called: Quadratic Equations

Which of the following are Quadratic Equations? y = x + 3 It’s degree is 2 y = x2 ....WHY? y = 2x – 4 It’s degree is 2 y = x2 + 2x – 3 ….WHY?

Find the factors of c that add to b Factoring Quadratic Equations Remember: Quadratic Equations have a degree of 2 Quadratics ax2 + bx + c Find the factors of c that add to b “Factors” are the numbers you multiply to get another number 1 x 6 and 2 x 3 The (+) factors of 6 are: The (-) factors of 6 are: -1 x -6 and -2 x -3

How to Factor Quadratic Equations Example 1 x2 + x + 7 7 12 12 1 x 12 =12 -1 x -12 = 12 2 x 6 = 12 -2 x -6 = 12 3 x 4 = 12 -3 x -4 = 12 Write down all the factor pairs of ___. (x )(x ) What goes with the x? 1 Positive Negative From this list, choose the pair that adds up to ___ 2 3 + 4 = 7 (x + 3)(x + 4) (x + )(x + ) 3 Put these numbers into brackets

(x + 3) (x + 4) x(x + 4) + 3(x + 4) x(x) + x(4) + 3(x) + 3(4) PROOF: x2 + 7x + 12 = (x + 3) (x + 4) (x + 3) (x + 4) x(x + 4) + 3(x + 4) x(x) + x(4) + 3(x) + 3(4) x2 + 4x + 3x + 12 x2 + 7x + 12 Factor: Factor: Combine like terms:

How to Factor Quadratic Equations Example 2 x2 + x + 6 6 (x )(x ) What goes with the x? 8 8 1 x 8 =8 -1 x -8 = 8 2 x 4 = 8 -2 x -4 = 8 Write down all the factor pairs of ___. 1 Positive Negative From this list, choose the pair that adds up to ___ 2 2 + 4 = 6 3 Put these numbers into brackets (x + 2)(x + 4)

How to Factor Quadratic Equations Example 2 x2 x -3 -3 -4 -4 -1 x 4 = -4 -2 x 2 = -4 1 x -4 = -4 2 x -2 = -4 Write down all the factor pairs of ___. 1 (x )(x ) What goes with the x? From this list, choose the pair that adds up to ___ 2 1 + -4 = -3 3 Put these numbers into brackets (x - 4)(x + 1)

1 x2 + 5x + 6 2 x2 - x – 6 3 x2 + 8x + 12 4 x2 + x – 12 5 x2 - 8x + 15 7 x2 - 3x – 18 8 x2 - 10x – 24 9 x2 + 8x + 16 10 x2 - 4x – 60

1 x2 + 5x + 6 (x + 3)(x + 2) 2 x2 - x – 6 (x – 3)(x + 2) 3 4 x2 + x – 12 (x – 3)(x + 4) 5 x2 - 8x + 15 (x – 3)(x – 5) 6 x2 + 3x – 21 (x + 7)(x – 4) 7 x2 - 3x – 18 (x – 6)(x + 3) 8 x2 - 10x – 24 (x - 12)(x + 2) 9 x2 + 8x + 16 (x + 4)(x + 4) 10 x2 - 4x – 60 (x - 10)(x + 4)

(x )(x ) What goes with the x?

(x - 3) (x - 2) x(x - 2) -3(x - 2) x(x) + x(-2) - 3(x) - 3(-2) Factor the following: x2 - 5x + 6 = Solution: x2 - 5x + 6 = (x - 3) (x - 2) (x - 3) (x - 2) x(x - 2) -3(x - 2) x(x) + x(-2) - 3(x) - 3(-2) x2 - 2x - 3x + 6 x2 - 5x + 6 Factor: Factor: Combine like terms: