HIGH SCHOOL MATH FACTORING. Ask Yourself the following questions… FACTORINGFACTORING 1Is there a common factor? Example: 6x 2 + 8x = 2x 1. What is the.

Slides:

Advertisements

Similar presentations

Factoring the Sum & Difference of Two Cubes

Advertisements

Perfect Square Trinomials. Form for Perfect Square Trinomials: a 2 + 2ab + b 2 OR a 2 – 2ab + b 2.

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Read as “plus or minus square root of a.”

(2.8) Factoring Special Products OBJECTIVE: To Factor Perfect Square Trinomials and Differences of Squares.

SUBTRACTING INTEGERS Math 7 Subtracting Integers Learn the rules for subtracting integers Recall rules for adding integers Several examples.

Table of Contents Factoring - Perfect Square Trinomial A Perfect Square Trinomial is any trinomial that is the result of squaring a binomial. Binomial.

Essential Question: How is FOIL related to factoring?

Math 20-1 Chapter 4 Quadratic Equations

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Solving Quadratics by Completing the Square, continued Holt Chapter 5 Section 4.

EXAMPLE 1 Factor ax 2 + bx + c where c > 0 Factor 5x 2 – 17x + 6. SOLUTION You want 5x 2 – 17x + 6 = (kx + m)(lx + n) where k and l are factors of 5 and.

Chapter 9 Polynomials and Factoring A monomial is an expression that contains numbers and/or variables joined by multiplication (no addition or subtraction.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

Monomials and Polynomials

Holt McDougal Algebra Completing the Square Solve quadratic equations by completing the square. Write quadratic equations in vertex form. Objectives.

5-4 Factoring Quadratic Expressions Objectives: Factor a difference of squares. Factor quadratics in the form Factor out the GCF. Factor quadratics with.

Objectives Solve quadratic equations by completing the square.

Algebra 2: Unit 5 Continued

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Solve Notice that if you take ½ of the middle number and square it, you get the last number. 6 divided by 2 is 3, and 3 2 is 9. When this happens you.

Square Roots/Addition

Multiply (2n + 3)(n + 4) 2n² + 8n + 3n n² + 11n + 12

Factoring - Perfect Square Trinomial A Perfect Square Trinomial is any trinomial that is the result of squaring a binomial. Binomial Squared Perfect Square.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

PERFECT SQUARE TRINOMIALS

Ch. 4.4 Factor Quadratic Equation I can find common binomial factors of quadratic expression with lead coefficient of 1 Do Now: On a suspension bridge,

FACTORING – Difference of Squares Factoring difference of squares is probably the easiest factoring you will encounter. The wording difference of squares.

Radicals (Square Roots). = 11 = 4 = 5 = 10 = 12 = 6 = 7 = 8 = 9 = 2.

Do Now: Multiply 1) (x+8)(x+4) 2) (x-8)(x-3) 3) (x-8)(x+1) 4) (x+9)(x-5) Aim: How Do We Factor Trinomials?

Completing the Square Solving Quadratics By Completing the Square Must be a perfect Square.

Essential Question: How is the process of completing the square used to solve quadratic equations? Students will write a summary of how they use completing.

Math in the Workplace Negative numbers.

Standard Form of a Quadratic Equation: y = ax 2 + bx + c a is the coefficient of the 1st term b is the coefficient of the 2nd term c is the coefficient.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 6.3 Factoring Trinomials of the form x 2 + bx + c.

Factoring Trinomials of the Type: ax 2 + bx + c Most trinomials can be factored even when the leading coefficient is something other than 1. Examples of.

Unit 5 Solving Quadratics By Square Roots Method and Completing the Square.

Box Method for Factoring Factoring expressions in the form of.

Factoring Polynomials Factoring is the process of changing a polynomial with TERMS (things that are added or subtracted) into a polynomial with THINGS.

5-4 Factoring Quadratic Expressions Hubarth Algebra II.

Greatest Common Factor To factor a polynomial whose terms have a common factor: Find the greatest common factor. Divide by the common factor. The common.

Solve Quadratic Functions by Completing the Square

2-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Solve Quadratic Equations by Completing the Square

Factoring the Sum & Difference of Two Cubes

Multiply (x+3)(2x-7) Factor 3. 42x – 7

Objectives Solve quadratic equations by completing the square.

Solving Quadratics By Completing the Square Part 2

Objectives Solve quadratic equations by completing the square.

Unit 4: Coordinate Geometry

Factoring the Difference of Two Squares

What is Factoring? Breaking apart a polynomial into the expressions that were MULTIPLIED to create it. If a Polynomial can not be factored, it is called.

Factoring the Sum & Difference of Two Cubes

9.3 Solve Quadratics by Completing the Square

AA Notes 4.3: Factoring Sums & Differences of Cubes

AA-Block Notes 4.4: Factoring Sums & Differences of Cubes

Factoring GCF and DOTS.

Quadratic Equations and Functions

Sign Rule: When the last term is NEGATIVE…

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

Factoring Trinomials.

Multiplying and Dividing Radical Expressions

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

2.3 Factor and Solve Polynomial Expressions

Dividing Radical Expressions

Factoring Polynomials

5.4 – Factoring ax2 + bx + c.

Presentation transcript:

HIGH SCHOOL MATH FACTORING

Ask Yourself the following questions… FACTORINGFACTORING 1Is there a common factor? Example: 6x 2 + 8x = 2x 1. What is the common factor? 2. Remove the common factor. 3. Divide each elements of the expression by the common factor. ( ) ( 3x + 4 ) = 2x

Ask Yourself the following questions… FACTORINGFACTORING 2 Is there the difference between two squares? Example: 4x 2 – 81 =(2x 9 ) ( 2x 9 ) =( ) ( ) How to determine if something is a “Difference of Two Squares” 1. Is the first term a perfect square? 2. Is the second term a perfect square? 3. Is there a negative sign in the middle? Then the expression is a Difference of Two Squares” 1. Use the Two Factor Method 2. Take the square root of the 1 st and the square root of the 2 nd 3. Use opposite signs in the middle =(2x + 9 ) ( 2x - 9 )

Ask Yourself the following questions… FACTORINGFACTORING 3Is there a perfect square? Example: x 2 + 8x + 16 How to determine if something is a “Perfect Square” 1.Is the first term a perfect square? 2.Is the last term a perfect square? 3.Recall: ax 2 + bx + c = 0 4.Does ( ½ b ) 2 = c ? Then the expression is a Perfect Square” 1.Set up the factor 2.Take the square root of the 1 st term and the square root of the last term 3. Use the sing of the middle term and place it between the square roots = ( ) 2 = ( x 4 ) 2 = ( x + 4 ) 2

Ask Yourself the following questions… FACTORINGFACTORING 4Is the coefficient of the x 2 ’d term = 1? Example: = ( ) ( ) x 2 – 7x Use the two factor method 2. Factor the 1 st term of the expression 3. Determine the signs of the factors 4. Determine the values of the2 nd term = ( x ) ( x ) = ( x - ) ( x - ) To determine the Signs of the Factors Recall: ax 2 + bx + c = 0 1. Consider the sign of the “c” term 2. If the sign is + then both signs will be the SAME and the factors will both have the sign of the “b” term 3. If the sign is – then both signs will be DIFFERENT and the higher number will take the sign of the “b” term To determine the Values of the Second Term Recall: ax 2 + bx + c = 0 1.What two numbers multiplied together will give the “c” term * = c 2. What same two numbers will give the “b” term + = b = ( x - 5 ) ( x - 2 )

Ask Yourself the following questions… FACTORINGFACTORING 5Is the coefficient of the x 2 ‘ d term ≠ 1 Example: 6x 2 + 5x Factor by “Grouping” = 6x 2 +5x - 4 = 6x 2 + 8x – 3x - 4 Recall ! 6x 2 + 5x – 4 1.The signs will be different 2.The larger number will be + Recall ! 6x 2 + 5x – 4 1. What 2 # ’ s multiplied together will give (6 * -4), -24 ? 2. What same 2 # ’ s added together will give 5 ? = 2x (3x + 4 ) – 1 (3x + 4) = (3x + 4 ) (2x - 1) 2. Determine the factors of the middle term 4. Remove the binomial Common Factor 3. Remove the common factor from the 2 groups

FACTORINGFACTORING

Is there a common factor? Is there the difference of two squares? Is there a perfect square? Is the coefficient of the x 2 ’d term = 1? Is the coefficient of the x 2 ’d term ≠ 1?