Answers to Unit 1, Lesson 1 Exercises

Slides:

Advertisements

Similar presentations

Factoring trinomials ax² + bx +c a = any number besides 1 and 0

Advertisements

Factoring Trinomials of the Type ax2 + bx + c

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

2-4 completing the square

EXAMPLE 4 Finding the GCF of Monomials

Factoring Special Cases. Factoring by Grouping. What you’ll learn To factor perfect square trinomials and differences squares. To factor higher degree.

Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6,

Essential Question: How do you factor a trinomial and how is it used to solve a quadratic equation? Students will write a summary that describes factoring.

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

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF.

PATTERNS, ALGEBRA, AND FUNCTIONS

Section 4.4 – Factoring Quadratic Expressions Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given.

5.4 Factoring Polynomials Alg 2. The GCF is 5ab. Answer: Distributive Property Factor Factoring with GCF.

Lesson 5-11 Using Several Methods of Factoring

5-4 Factoring M11.D A Objectives: 1) To factor polynomials with a common factor. 2) To identify and factor trinomial squares. 3) To factor the.

4.4 Factoring Quadratic Expressions P Factoring : Writing an expression as a product of its factors. Greatest common factor (GCF): Common factor.

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

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

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Quadratic Function A function that can be written in standard form; f(x) = ax 2 + bx + c where a ≠ 0.

Chapter 11 Polynomials 11-1 Add & Subtract Polynomials.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

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 -

Factoring trinomials ax² + bx +c a = any number besides 1 and 0.

Warm Up:. Factoring Polynomials Number of TermsFactoring TechniqueGeneral Pattern Any number of terms Greatest Common Factora 3 b 2 + 2ab 2 = ab 2 (a.

Factoring – Day 4 Factoring Trinomials Objective: To factor trinomials whose quadratic coefficient is 1.

Algebra 2 Ch.5 Notes Page 33 P Factoring Quadratic Expressions (Part 1)

5-4 Factoring Quadratic Expressions Big Idea: -Factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference.

World 1-9 Completing the Square.

Warmup 1.) 16x2 – 81 2.) 3x ) 9x7 + 15x3 -18 x5 4.) 2x2 + 5x - 12.

Notes Over 10.8 Methods of Factoring Binomial Trinomial

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

Factor It’s a big deal!.

Section 6.4: Factoring Polynomials

Solve Polynomial Equations in Factored Form

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.

Algebra II with Trigonometry Mrs. Stacey

Chapter 5 – Quadratic Functions and Factoring

Factoring Quadratic Expressions

Answers to Homework 8) (x + 6)(2x + 1) 10) (2n – 3)(2n – 1) 12) (2r – 5)(3r – 4) 14) (5z – 1)(z + 4) 16) (2t – 1)(3t + 5) 18) (4w + 3)(w – 2) 20) (2x +

Algebra 1 Warm ups #5 Find the GCF for #1. Factor #s

Factoring Polynomials

Do Now: Get your homework and green sheet out for Ms. Taylor to stamp.

Factoring GCF and Trinomials.

2 Terms 3 Terms 4 Terms Always look for a GCF! Always look for a GCF!

Warmups – factor. 1) 2xy3 – 6x2y 2) x2 – 12x ) 4y2 + 36y + 81

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

Keeper 1 Honors Calculus

Homework Questions.

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

Chapter 2: Factoring Chapter 2: Limits Chapter 3: Continuity.

Factoring GCF and DOTS.

Example 1 Write an Equation Given Slope and a Point

Review: 6.5b Mini-Quiz 1. Solve: 9x2 – 100 = 0.

Factoring by GCF CA 11.0.

Factoring Trinomials of the Type ax2 + bx + c

Warm Up Factor the following: a) b).

Warm-up #23 (Monday, 10/26) Simplify (x+2)(3x – 4)

The constant is always the square of half Or

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

3.4 Solve by Factoring (Part 1)

2.3 Factor and Solve Polynomial Expressions

Review: 6.5c Mini-Quiz 1. Solve: 4x2 – 40 = –27x.

Algebra II with Trigonometry Mr. Agnew

Get Started!! x  , y  ______.

Checklist: Factoring Portfolio Page -- Algebra 2

Factoring Quadratic Expressions

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

Warmup 1.) 16x2 – 81 2.) 3x ) 9x7 + 15x3 -18 x5 4.) 2x2 + 5x - 12.

Special Cases and Grouping

Presentation transcript:

Answers to Unit 1, Lesson 1 Exercises 3x2 – 5x + 6 -4x2 – 7x – 17 4y2 + y + 7 7z – 10 2x3 – 2x2 + 6x -12u2 + 3u -15x3 – 5x2 + 10x

Answers to Unit 1, Lesson 1 Exercises x2 + 8x + 15 8x2 + 14x + 3 x2 – 36 9x2 – y2 x2 + 4x + 4 9 – 30x + 25x2 u2 + v2 – 2uv + 4u – 4v + 4 a2 – b2 – 4a + 4

Answers to Unit 1, Lesson 1 Exercises 8x3 – 12x2y + 6xy2 – y3 8x3 – 84x2 + 294x – 343 x3 + 2x2 – 5x + 12 x2 – 2 x3 – 8 12

Unit 1, Lesson 2 : Factoring using GCF and Factoring Trinomials Factoring is rewriting an expression as the product of its factors. The greatest common factor (GCF) of an expression is the common factor with the greatest coefficient and the greatest exponent.

Examples: Factor . 1. 4x2 + 20x – 12 2. 9n2 – 24n

You try: 9x3 + 18x2 – 3x 7p2 + 21

Factoring Trinomials ax2 + bx + c , when a = 1 Examples: 5. x2 + 8x + 7 6. x2 – 17x + 72 7. x2 – x – 12

You try: x2 – 11x + 24 x2 + 3x – 10 x2 + 18x + 32

Factoring Trinomials ax2 + bx + c , when a  1 Examples: 3x2 – 16x + 5 12. 4x2 – 4x – 15

You try: 4x2 + 7x + 3 4x2 + 5x – 6

Perfect Square Trinomials 4x2 + 12x + 9 16. 9x2 – 6x + 1

Difference of Squares: a2 – b2 = (a – b)(a + b) 17. x2 – 64 16. 4x2 – 49

Factoring Completely Always look for GCF first!! 9x2 – 36 16x2 – 80x + 100

Homework Practice 5-4 odds only!