8-7 Factoring Special Cases

Slides:

Advertisements

Similar presentations

Bellringer part two Simplify (m – 4) 2. (5n + 3) 2.

Advertisements

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

Warm Up. Essential Question: How do you factor a polynomial without a middle term?

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

9.1 Adding and Subtracting Polynomials

Factoring Polynomials

Polynomials and Factoring Review By: Ms. Williams.

Factoring Review EQ: How do I factor polynomials?.

Multiplying Polynomials. Multiply monomial by polynomial.

Purpose: To factor polynomials completely. Homework: P odd.

Multiplying Polynomials *You must know how to multiply before you can factor!”

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.

Special Products Difference of Two Squares Perfect Square Trinomials

Factor the following special cases

Warm-Up #2 Multiply these polynomials. 1) (x-5) 2 2) (8x-1) 2 3. (4x- 3y)(3x +4y) Homework: P5 (1,3,5,11,13,17,27,33,41, 45,49,55,59,63,71,73,77) Answers:

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.

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

Warm Ups Term 2 Week 3. Warm Up 10/26/15 1.Add 4x 5 – 8x + 2 and 3x x – 9. Write your answer in standard form. 2.Use the Binomial Theorem to expand.

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

Chapter 11 Polynomials 11-1 Add & Subtract Polynomials.

Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +

Adding and Subtracting Polynomials

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

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

Use patterns to multiply special binomials.. There are formulas (shortcuts) that work for certain polynomial multiplication problems. (a + b) 2 = a 2.

Do Now!. Special Products of Binomials You will be able to apply special products when multiplying binomials.

Factoring Completely.

use patterns to multiply special binomials.

Section 6.4: Factoring Polynomials

Factoring Polynomials

Example: Factor the polynomial 21x2 – 41x No GCF Puzzle pieces for 21x2 x, 21x 3x, 7x Puzzle pieces for 10 1, 10 2, 5 We know the signs.

Factoring Special Products

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

Factoring the Difference of Two Squares

Factor each trinomial x2 + 40x + 25 (4x + 5)(4x + 5)

8.6 Choosing a Factoring Method

Special Cases in Factoring Polynomials

Chapter 6 Section 3.

Factor. x2 – 10x x2 – 16x + 1 Multiply. 3. (4x- 3y)(3x +4y)

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 +

BELL-WORK (x – 5)(x + 5) = x2 – 25 (b) (3x – 2)(3x + 2) = 9x2 – 4

Factoring trinomials ax² + bx +c a = 1

a*(variable)2 + b*(variable) + c

Factoring Differences of Squares

Factoring Differences of Squares

Polynomials and Polynomial Functions

a*(variable)2 + b*(variable) + c

AA Notes 4.3: Factoring Sums & Differences of Cubes

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

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

a*(variable)2 + b*(variable) + c

Example 2A: Factoring by GCF and Recognizing Patterns

Warm Up: Solve the Equation 4x2 + 8x – 32 = 0.

Chapter 6 Section 3.

Factoring Differences of Squares

Objectives Factor perfect-square trinomials.

8-5 FACTORING TRINOMIALS

Factoring Special Products

8-6 Factoring trinomials (a>1)

(B12) Multiplying Polynomials

8-4 Multiplying Special Cases

Factoring Perfect Square Trinomials

6.6 Factoring Polynomials

Chapter 6 Section 3.

Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

Warm Up answers 1. x 2. 3x²y – 8xy² 3. 7x² - 3x 4. 1 term 5. 2 terms

Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1)

6.2 Difference of 2 Squares.

5.10 Multiplying Binomials: Special Products

Factoring Polynomials

Presentation transcript:

8-7 Factoring Special Cases Please work on the following problems on your notes (start before the bell rings): Warm up: #1: Multiply: (x – 5)(x + 5) #2: - 9y4 + 2x4y a) Name polynomial (by terms) b) Name polynomial (by degree) c) Factor #3: Factor x3 + 2x2 + 9x + 18

8-7 Factoring Special Cases ANSWERS #1: Multiply: (x – 5)(x + 5) x2 + 5x – 5x – 25 x2 – 25 #2: - 9y4 + 2x4y a) Name polynomial (by terms) Binomial b) Name polynomial (by degree) Quintic c) Factor -y(9y3 – 2x4) #3: Factor x3 + 2x2 + 9x + 18 x 2 x2 x3 2x2 9x 18 9 GCF: -y (x2 + 9)(x + 2) OR y(-9y3 + 2x4)

(Review) Multiply 1) (x + 3) (x – 3) x2 – 3x + 3x – 9 Ok…Do QUICKLY!! What do you notice??? Ok…Do QUICKLY!! 4) (x + 7) (x – 7) x2 – 49 How about.. 5) (2x – 8)(2x + 8) 4x2 – 16x + 16x – 64 4x2 – 64

Difference of Squares OLD: Multiply (a + b)(a – b) = a2 – b2 NEW: Factor difference of squares a2 – b2 = (a + b)(a – b) Can take square root of both numbers/letters Minus sign in the middle

Square Roots to Know

TOO: Is it a Difference of Squares? x2 – 4 9x2 – 1 2x2 – 4 2x2 – 8 x2 + y2 x3 – 25 9xy – y2 -16 + x2 -4 – 16x2 x4 – 81 YES NO √2 YES 2(x2 – 4) NO Adding NO x3 NO x YES x2 – 16 NO -4(1 + 4x2) YES √x4 = x2

Ex: FACTOR (difference of squares) (x + 2)(x – 2) (3x + 1)(3x – 1) 2(x2 – 4) 2(x + 2)(x – 2) 4) x2 – 16 (x + 4)(x – 4) 5) (x2 + 9)(x2 – 9) (x2 + 9)(x + 3)(x – 3) HINT: 2(x2 – 4) HINT: x2 – 16

TOO - Review everything!  x 1 6) Factor 3x2 – 3 3(x2 – 1) 3(x + 1)(x – 1) 7) Factor x3y + x x(x2y + 1) 8) Factor 6x3 + 6x2 + 8x + 8 9) Factor 4x3 + 12x2 – 9x – 27 6x2 6x3 6x2 GCF 3 8 8x 8 GCF x (6x2 + 8)(x + 1) GCF 2 2(3x2 + 4)(x + 1) (4x2 – 9 )(x + 3) Diff of sq (2x +3)(2x – 3)(x + 3)

Delta Math Homework Due Mon

Factor using 1) GCF 2) Grouping/Box 3) X – BOX 4) Difference of Squares 5) Perfect Square Trinomial Question #’s Answer 16x2 – 40x – 24 81x4 – 16y4 y2 – 6y – 16 24x2 – 8 2x3 – 3x2 + 5x n2 + 2n + 3mn + 6m t3 – t2 + t – 1 4a3 + 8a2 + 4a 5x2 – 45y2 1 – 8u + 16u2 1&3 4&4 3 1 2 1&5 1&4 5 8(2x + 1)(x – 3) (9x2 + 4y2)(3x + 2y)(3x – 2y) (y – 8)(y + 2) 8(3x2 – 1) x(2x2 – 3x + 5) (n + 3m)(n + 2) (t – 1)(t2 + 1) 4a(a + 1)2 5(x + 3y)(x – 3y) (1 – 4u)2