Difference of Squares Chapter 8.8. Difference of Squares (Definition)

Slides:

Advertisements

Similar presentations

Polynomials and Factoring

Advertisements

Factoring Trinomials of the form

Ch. 5 Polynomials, Polynomial Functions, & Factoring

Factoring Trinomials of the form x 2 + bx + c Chapter 5.3.

Bell Ringer #4 Quad Card Directions: Draw the quad card on your paper, but replace each definition with the vocabulary term that it matches. Rewriting.

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

Magicians Factoring Expressions -Greatest Common Factor (GCF) -Difference of 2 Squares.

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

Warm Up Factor: Homework Check 6.4 Factoring.

5.4 Factoring Quadratic Expressions. WAYS TO SOLVE A QUADRATIC EQUATION ax² + bx + c = 0 There are many ways to solve a quadratic. The main ones are:

Over Lesson 8–4 A.A B.B C.C D.D 5-Minute Check 1 (2c – 9)(c – 4) Factor 2c 2 – 17c + 36, if possible.

8.5 – Factoring Differences of Squares. Recall: Recall: Product of a Sum & a Difference.

1. The height of an object launched t seconds is modeled by h(t) = -16t t Find the vertex and interpret what it means. What is the height of.

Polynomials and Factoring Review By: Ms. Williams.

Factoring Polynomials

Factoring, Difference of Two Squares

Warm-up over Lesson 5-1.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–7) CCSS Then/Now New Vocabulary Key Concept: Difference of Squares Example 1:Factor Differences.

Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

MA.912.A.4.2: Add, subtract, and multiply polynomials. Which of the following expressions is equivalent to (5x − 3) 2 ? A. 25x 2 − 30x + 9 B. 25x 2 −

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 6 Factoring.

Multiplying Polynomials. Multiply monomial by polynomial.

8.8: FACTORING BY GROUPING: Higher Degree Polynomials: Polynomials with a degree higher than 2.

Factoring Checklist Works every time!. 1. Check to see if there is a GCF. If so, factor it out. 3xy² + 12xy.

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

Algebra I Notes Section 9.6 (A) Factoring ax 2 + bx + c With Leading Coefficient ≠ 1.

EOQ REVIEW #2 Hoops Exponents RadicalsPolynomials Factoring Word Problems Q 1 pt. Q 2 pt. Q 3 pt. Q 4 pt. Q 5 pt. Q 1 pt. Q 2 pt. Q 3 pt. Q 4 pt. Q 5.

Splash Screen. Then/Now You multiplied polynomials by monomials. Multiply binomials by using the FOIL method. Multiply polynomials by using the Distributive.

Factoring Binomials Algebra Lesson 9-5. Let’s Review 1) 6ab + 3a 2) 5x 3 – 3y 2 3) 2c 4 – 4c 3 + 6c 2 4) 4w 4n + 12w 4n+3.

Aim: How do we factor polynomials completely? Do Now: Factor the following 1. 2x 3 y 2 – 4x 2 y 3 2. x 2 – 5x – 6 3. x 3 – 5x 2 – 6x.

12.0 Polynomial Vocabulary. Term  Numbers or variables separated by _____ or _____ signs.  Examples:

Tuesday, November 8 th Set up a new assignment sheet 4.3: Greatest Common Factors.

Chapter 11 Polynomials 11-1 Add & Subtract Polynomials.

FFF FFF i v e o r m s o f a c t o r i n g 1.Greatest Common Factor (GCF) Ex 1 10x 2 y 3 z - 8x 4 y 2 2x 2 y 2 (5yz - 4x 2 ) Ex 2 15a 2 b 5 + 5ab 2 -

Adding and Subtracting Polynomials

Bellwork: Factor Each. 5x2 + 22x + 8 4x2 – 25 81x2 – 36 20x2 – 7x – 6

Multiplying Powers Dividing Powers Zero ExponentsNegative.

Monday’s Homework 1.Any questions? 2.Make sure the homework is 100% complete. Incomplete work will NOT be accepted.

Factoring Factoring in the format ax2+bx+c Problem 1 X 2 + 7x + 10.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–1) Then/Now Example 1:LCM of Monomials and Polynomials Key Concept: Adding and Subtracting.

A.A B.B C.C D.D 5Min 2-1 A.Yes; the expression involves only one variable. B.Yes; the expression is the product of a number and variables. C.No; the expression.

Homework (Tuesday, 11/3) Lesson 2.03 packet page 4 and 5.

Quiz for Solving Mathematical Equations Megan Reichert Click to Start the Quiz!

Splash Screen. Then/Now You wrote equations of lines using information about their graphs. Write the equation of a circle. Graph a circle on the coordinate.

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

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–3) CCSS Then/Now Key Concept: Square of a Sum Example 1:Square of a Sum Key Concept: Square.

Splash Screen Unit 8 Quadratic Expressions and Equations EQ: How do you use addition, subtraction, multiplication, and factoring of polynomials in order.

Section 6.4: Factoring Polynomials

Quadratic Expressions and Equations

Factoring Polynomials

F i v e o r m s o f a c t o r i n g For Forms 1 - 3, do the examples on your paper then use the PowerPoint to check your answers Do not do Form 4.

Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2

Factoring Polynomials by Grouping

8.6 Choosing a Factoring Method

Practice Factor each polynomial 1. 3y2 + 2y + 9y + 6

Before: February 5, 2018 Factor each polynomial. Check your answer.

Warm-Up #22 (3m + 4)(-m + 2) Factor out ( 96

4.4 Factoring Polynomials

Answers to Unit 1, Lesson 1 Exercises

Factoring by GCF CA 11.0.

Factoring by GCF CA 11.0.

Factoring the Difference of

1) Which pair of factors of 8 has a sum of 9?

4.6 Factoring Polynomials

5.5 – Completing the Square

Objective Factor polynomials by using the greatest common factor.

Factoring Polynomials.

Objective Factor polynomials by using the greatest common factor.

2.3 Factor and Solve Polynomial Expressions

F i v e o r m s o f a c t o r i n g.

Presentation transcript:

Difference of Squares Chapter 8.8

Difference of Squares (Definition)

Factor m 2 – 64. m 2 – 64 = m 2 – 8 2 Write in the form a 2 – b 2. = (m + 8)(m – 8)Factor the difference of squares. Answer: (m + 8)(m – 8) Difference of Squares Ex#1

Factor 16y 2 – 81z 2. 16y 2 – 81z 2 = (4y) 2 – (9z) 2 Write in the form a 2 – b 2. = (4y + 9z)(4y – 9z)Factor the difference of squares. Answer: (4y + 9z)(4y – 9z) Difference of Squares Ex#2

A.(5a + 6b)(5a – 6b) B.(5a + 6b) 2 C.(5a – 6b) 2 D.25(a 2 – 36b 2 ) Factor the binomial 25a 2 – 36b 2. Difference of Squares - Your Turn!

Factor 3b 3 – 27b. If the terms of a binomial have a common factor, the GCF should be factored out first before trying to apply any other factoring technique. = 3b(b + 3)(b – 3)Factor the difference of squares. 3b 3 – 27b = 3b(b 2 – 9)The GCF of 3b 2 and 27b is 3b. = 3b[(b) 2 – (3) 2 ]Write in the form a 2 – b 2. Answer: 3b(b + 3)(b – 3) Difference of Squares with a GCF Ex#1

Factor 9x 5 – 36x. Answer: 9x(x 2 – 2)(x 2 + 2) 9x 5 – 36x= 9x(x 4 – 4)Factor out the GCF. = 9x[(x 2 ) 2 – 2 2 ]Write x 2 – 4 in a 2 – b 2 form. = 9x(x 2 – 2)(x 2 + 2)Factor the difference of squares. Difference of Squares with a GCF Ex#2

A.3x(x 2 + 3)(x 2 – 4) B.3x(x 2 + 2)(x 2 – 2) C.3x(x 2 + 2)(x + 2)(x – 2) D.3x(x 4 – 4x) Factor 3x 5 – 12x. Difference of Squares with a GCF – Your Turn!

Factor 256 – n – n 4 = 16 2 – (n 2 ) 2 Write 256 – n 4 in a 2 – b 2 form. = (16 + n 2 )(16 – n 2 )Factor the difference of squares. = (16 + n 2 )(4 2 – n 2 )Write 16 – n 2 in a 2 – b 2 form. = (16 + n 2 )(4 – n)(4 + n)Factor the difference of squares. Answer: (16 + n 2 )(4 – n)(4 + n) Difference of Squares with 2 “Differences”

A.(9 + d)(9 – d) B.(3 + d)(3 – d)(3 + d)(3 – d) C.(9 + d 2 )(9 – d 2 ) D.(9 + d 2 )(3 + d)(3 – d) Factor 81 – d 4. Difference of Squares with 2 “Differences” – Your Turn!

Factor 6x x 2 – 24x – x x 2 – 24x – 120Original polynomial = 6(x 3 + 5x 2 – 4x – 20)Factor out the GCF. = 6[(x 3 – 4x) + (5x 2 – 20)]Group terms with common factors. = 6[x(x 2 – 4) + 5(x 2 – 4)]Factor each grouping. = 6(x 2 – 4)(x + 5)x 2 – 4 is the common factor. = 6(x + 2)(x – 2)(x + 5)Factor the difference of squares. Answer: 6(x + 2)(x – 2)(x + 5) Difference of Squares Extended Example

A.5(x 2 – 9)(x + 5) B.(5x + 15)(x – 3)(x + 5) C.5(x + 3)(x – 3)(x + 5) D.(5x + 25)(x + 3)(x – 3) Factor 5x x 2 – 45x – 225. Difference of Squares Extended Example – Your Turn!

HOMEWORK 8.8 #’s all