Identifying & Factoring: x 2 + bx + c
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1 Identifying & Factoring: x 2 + bx + c Apr 13 11:04 AM 1
2 May 16 8:52 AM 2
3 A polynomial that can be simplified to the form ax + bx + c, where a 0, is called a quadratic polynomial. Linear term. Quadratic term. Constant term. Identifying Polynomials 3
4 A quadratic polynomial in which b 0 and c 0 is called a quadratic trinomial. If only b=0 or c=0 it is called a quadratic binomial. If both b=0 and c=0 it is a quadratic monomial. Examples: Choose all of the description that apply. Cubic Quadratic Linear Constant Trinomial Binomial Monomial Identifying Polynomials 4
5 1 Choose all of the descriptions that apply to: A B C D E F Quadratic Linear Constant Trinomial Binomial Monomial Pull Identifying Polynomials 5
6 2 Choose all of the descriptions that apply to: A B C D E F Quadratic Linear Constant Trinomial Binomial Monomial Pull Identidying Polynomials 6
7 3 Choose all of the descriptions that apply to: A B C D E F Quadratic Linear Constant Trinomial Binomial Monomial Pull Identifying Polynomials 7
8 4 Choose all of the descriptions that apply to: A B C D E F Quadratic Linear Constant Trinomial Binomial Monomial Pull Identifying Polynomials 8
9 Simplify. **Complete the following. Turn in your answers. Answer Bank 1) (x + 2)(x + 3) = 2) (x 4)(x 1) = 3) (x + 1)(x 5) = x 2 + 5x + 6 x 2 4x 5 x 2 5x + 4 x 2 + 4x 12 4) (x + 6)(x 2) = Slide each polynomial from the circle to the correct expression. RECALL What did we do?? Look for a pattern!! 9
10 May 9 8:54 AM 10
11 May 9 8:54 AM 11
12 May 9 8:55 AM 12
13 May 9 8:55 AM 13
14 To Factor a Trinomial with a Lead Coefficient of 1 Recognize the pattern: Factors of 6 have the same signs. Factors of 6 Sum to 5? 1, 6 7 Factors of 6 add to +5. Both factors must be positive. 2,
15 To Factor a Trinomial with a Lead Coefficient of 1 Recognize the pattern: Factors of 6 have the same signs. Factors of 6 Sum to 7? Factors of 6 add to 7. Both factors must be negative. 1, 6 7 2,
16 Examples: (x 8)(x 1) 16
17 5 The factors of 12 will have what kind of signs given the following equation? A B C D Both positive Both Negative Bigger factor positive, the other negative The bigger factor negative, the other positive Pull 17
18 6 The factors of 12 will have what kind of signs given the following equation? A B C D Both positive Both negative Bigger factor positive, the other negative The bigger factor negative, the other positive Pull 18
19 7 Factor A (x + 12)(x + 1) B (x + 6)(x + 2) C (x + 4)(x + 3) D (x 12)(x 1) E (x 6)(x 1) F (x 4)(x 3) Pull 19
20 8 Factor A (x + 12)(x + 1) B (x + 6)(x + 2) C (x + 4)(x + 3) D (x 12)(x 1) E (x 6)(x 1) Pull F (x 4)(x 3) 20
21 9 Factor A (x + 12)(x + 1) B (x + 6)(x + 2) C (x + 4)(x + 3) D (x 12)(x 1) E (x 6)(x 1) F (x 4)(x 3) Pull 21
22 10 Factor A (x + 12)(x + 1) B (x + 6)(x + 2) C (x + 4)(x + 3) D (x 12)(x 1) E (x 6)(x 2) F (x 4)(x 3) Pull 22
23 To Factor a Trinomial with a Lead Coefficient of 1 Recognize the pattern: Factors of 6 have the opposite signs. Factors of 6 Sum to 5? 1, 6 5 Factors of 6 add to 5. Larger factor must be negative. 2,
24 To Factor a Trinomial with a Lead Coefficient of 1 Recognize the pattern: Factors of 6 have the opposite signs. Factors of 6 Sum to 1? 1, 6 5 Factors of 6 add to +1. Larger factor must be positive. 2,
25 Examples 25
26 11 The factors of 12 will have what kind of signs given the following equation? A B C D Both positive Both negative Bigger factor positive, the other negative The bigger factor negative, the other positive Pull 26
27 12 The factors of 12 will have what kind of signs given the following equation? A B C D Both positive Both negative Bigger factor positive, the other negative The bigger factor negative, the other positive Pull 27
28 13 Factor A (x + 12)(x 1) B (x + 6)(x 2) C (x + 4)(x 3) Pull D (x 12)(x + 1) E (x 6)(x + 1) F (x + 4)(x 3) 28
29 14 Factor A (x + 12)(x 1) B (x + 6)(x 2) C (x + 4)(x 3) Pull D (x 12)(x + 1) E (x 6)(x + 1) F unable to factor using this method 29
30 15 Factor A (x + 12)(x 1) B (x + 6)(x 2) C (x + 4)(x 3) Pull D (x 12)(x + 1) E (x 6)(x + 1) F (x 4)(x + 3) 30
31 Mixed Practice Mixed Practice 31
32 16 Factor the following A (x 2)(x 4) B (x + 2)(x + 4) C (x 2)(x +4) D (x + 2)(x 4) Pull 32
33 17 Factor the following A (x 3)(x 5) B (x + 3)(x + 5) C (x 3)(x +5) Pull D (x + 3)(x 5) 33
34 18 Factor the following A (x 3)(x 4) B (x + 3)(x + 4) C (x +2)(x +6) D (x + 1)(x+12) 34
35 19 Factor the following A (x 2)(x 5) B (x + 2)(x + 5) C (x 2)(x +5) Pull D (x + 2)(x 5) 35
36 Steps for Factoring a Trinomial 1) See if a monomial can be factored out. 2) Need 2 numbers that multiply to the constant 3) and add to the middle number. 4) Write out the factors. There is no common monomial,so STEP factor: 1 STEP 2 STEP 3 STEP 4 36
37 Factoring Trinomials Assignment: The Apr 13 11:06 AM 37
38 Answer: The cat who joined the red cross because it wanted to be a first aid kit. May 2 8:27 AM 38
39 Homework: Complete the 1-1 Reteaching worksheet. May 2 8:38 AM 39
40 Apr 13 11:05 AM 40
41 Lab: 1. Complete the 10 question distributive property quiz. Work independently. Hand in when done. 2. Work on math essay 3. Prodigy Apr 13 11:06 AM 41
42 Apr 13 11:06 AM 42
43 May 11 8:14 AM 43
44 May 2 8:27 AM 44
Slide 1 / 128. Polynomials
Slide 1 / 128 Polynomials Slide 2 / 128 Table of Contents Factors and GCF Factoring out GCF's Factoring Trinomials x 2 + bx + c Factoring Using Special Patterns Factoring Trinomials ax 2 + bx + c Factoring
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1. Which pair of factors of 8 has a sum of 9? 1 and 8 2. Which pair of factors of 30 has a sum of. r 2 4r 45
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