Factoring Perfect Square

Slides:

Advertisements

Similar presentations

Multiplying Binomials

Advertisements

Factoring Polynomials.

Factoring Polynomials

Objective The student will be able to: factor perfect square trinomials. SOL: A.2c Designed by Skip Tyler, Varina High School.

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

10.7 Factoring Special Products

Math Notebook. Review  Find the product of (m+2) (m-2)  Find the product of (2y-3)^2.

Factoring Special Products Goal 1 Recognize Special Products Goal 2 Factor special products using patterns

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.

4.5 Supplemental Notes - Factoring Special Products - Solutions

Multiplying Positive & Negative Numbers. -6 x –4 = =

5.4 Special Products. The FOIL Method When multiplying 2 binomials, the distributive property can be easily remembered as the FOIL method. F – product.

Section 5.4 Factoring FACTORING Greatest Common Factor,

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.

6.3 Trinomial Squares Goals: To recognize a trinomial square and be able to factor it Remember to always factor out a common factor before you see if.

Multiply the following two polynomials: (x + 3)(x+3). x + 3 x2x2.

Warm-up Multiply. 1) 2) 3) 4). Factor. 1) 2) 3) 4) 5) 6) 7) Objective - To recognize and use the Difference of Squares pattern.

C ollege A lgebra Basic Algebraic Operations (Appendix A)

Factoring a polynomial means expressing it as a product of other polynomials.

Factoring General Trinomials Factoring Trinomials Factors of 9 are: REVIEW: 1, 93, 3.

Algebra 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first.

Factoring General Trinomials Factoring Trinomials Factors of 9 are: REVIEW: 1, 93, 3.

Objective - To recognize and factor a perfect square trinomial. Find the area of the square in terms of x. Perfect Square Trinomial.

Warm Up ~ 10-4~Factoring Sums and Differences of Squares Factor each polynomial: 1.x x Factor each perfect square. If not a perfect square,

 1. Square the first term.  2. Double the product of the two terms.  3. Square the last term.  Ex:  (2x – 1) 2  4x 2 - 4x + 1 Perfect square trinomial.

Objectives: Students will be able to…  Write a polynomial in factored form  Apply special factoring patterns 5.2: PART 1- FACTORING.

Section 5.5 (Easy Factoring) Perfect Square Trinomials & Differences of Squares  Review: The Perfect Square Trinomial Rules (A + B) 2 = A 2 + 2AB + B.

Page 452 – Factoring Special

WARM UP SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE EXACT ANSWER. DON’T ROUND.

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

Entry Task What is the polynomial function in standard form with the zeros of 0,2,-3 and -1?

Special Factoring Patterns Students will be able to recognize and use special factoring patterns.

Algebra 10.7 Factoring Special Products. Use the Patterns! (2x + 3) 2 (2p - 4) (2p + 4) (2x - y) 2 4x² + 12x + 9 4p² x² - 4xy + y² Perfect Square.

Types of factoring put the title 1-6 on the inside of your foldable and #7 on the back separating them into sum and cubes 1.Greatest Common Factor 2.Difference.

Objective - To recognize and use the factoring pattern, Difference of Squares. Multiply. 1) 2) 3) 4) Inner and Outer terms cancel!

Warm Up Factor out the GCF 1.-5x x x 3 +4x Factor 3. 4.

Difference of Two Perfect Squares

ALGEBRA 1 Lesson 8-7 Warm-Up ALGEBRA 1 “Factoring Special Cases” (8-7) What is a “perfect square trinomial”? How do you factor a “perfect square trinomial”?

Multiplying Polynomials “Two Special Cases”. Special Products: Square of a binomial (a+b) 2 = a 2 +ab+ab+b 2 = a 2 +2ab+b 2 (a-b) 2 =a 2 -ab-ab+b 2 =a.

Difference of Squares Recall that, when multiplying conjugate binomials, the product is a difference of squares. E.g., (x - 7)(x + 7) = x Therefore,

Objective - To factor trinomials in the form,

Entry Task What is the polynomial function in standard form with the zeros of 0,2,-3 and -1?

Factoring Perfect Square Trinomials and the Difference of Squares

Notes 8.7 – FACTORING SPECIAL CASES

Objectives Factor perfect-square trinomials.

Factoring Perfect Square Trinomials and the Difference of Squares

Do Now Determine if the following are perfect squares. If yes, identify the positive square root /16.

What numbers are Perfect Squares?

Factoring the Difference of Two Squares

Factoring Special Cases :

A Number as a Product of Prime Numbers

Objective - To factor trinomials in the form .

Objective - To factor trinomials in the form,

Factoring Polynomials

Factoring Special Products

Show What You Know! x2 + 4x – 12 5x2 + 19x x2 – 25x - 25

Lesson 9.1 How do you add and subtract polynomials?

Squares of Binomials Chapter 5 Section 5.6.

Perfect Square Trinomials

Factoring Polynomials

Objective - To factor trinomials in the form .

Objective The student will be able to:

Factoring Special Forms

Objectives Factor perfect-square trinomials.

Objective - To factor trinomials in the form .

Factoring Polynomials.

Factoring Special Products

Objective - To factor trinomials in the form,

Perfect Square Trinomial

Objective - To recognize and use the factoring pattern, Difference of Squares. Multiply. 1) 2) 3) 4) Inner and Outer terms cancel!

Presentation transcript:

Factoring Perfect Square Goal 1 Recognize perfect square Goal 2 Factor perfect square using patterns.

Recall what happens when you multiply the following: (x + 4)(x + 4) (x – 3)2 The results are called ____________________________.

Factoring a Perfect Square Trinomial OR It has to be exactly in this form to use this rule. When you have a base being squared plus or minus twice the product of the two bases plus another base squared, it factors as the sum (or difference) of the bases being squared.

Factor the perfect square trinomial: Example 1 Factor the perfect square trinomial: If you can recognize that it fits the form of a perfect square trinomial, you can save yourself some time. *Fits the form of a perfect square trinomial *Factor as the sum of bases squared

a b Does the middle term fit the pattern, 2ab? Yes, the factors are (a + b)2 :

a b Does the middle term fit the pattern, 2ab? Yes, the factors are (a - b)2 :

Example 2 Factor the following trinomials: x2 + 5x + 12 x2 + 6x + 9

Example 3 Factor the following trinomials: x2 + 8x + 16 4x2 + 12x + 9

Example 4 Factor the trinomial: