UNIT 2 – FACTORING QUADRATIC EXPRESSIONS

Date Lesson Text TOPIC Homework

Feb.

21 2.0 Opt

Getting Started Pg. 74 # 2 - 13

Feb.

22

2.1

2.1

Working with Quadratic Expressions Pg. 85 # 2, 3, 5 – 7, 10, 11, 13,

14

Feb.

23

2.2

2.2

Factoring Polynomials:

Common Factoring

Pg. 93 # 2, 3, 5 – 8, 10, 12. 15

Feb.

24

2.3

2.3

Factoring Quadratic Expressions:

x2 + bx + c

Pg. 99 #2, 3, 5 – 9, 12 - 14

Feb.

27

2.4

Mid-Chapter Review Pg. 103 # 1, 3 – 5, 7, 9 - 11

Feb.

28

2.5

2.4

Factoring Quadratic Expressions:

ax2 + bx + c QUIZ ( 2.1 - 2.3)

Pg. 109 # 2, 4 – 10, 13

Mar. 1 2.6

2.5

Factoring Quadratic Expressions:

Special Cases

Pg. 115 # 2 - 12

Mar. 2 2.7

Review for Unit 2 Test Pg. 120 # 1, 3 – 6, 8, 9, 11 – 13

15 - 19

Mar. 3 2.8

(20)

UNIT 2 TEST

MCF 3M Lesson 2.0 Getting Started

Ex. 1. Match each word with the expression that best illustrates its definition.

Ex. 2. Simplify each expression

a) 222 10122687 xxyxxyxxy

b) )2()97()82( aababba

Ex. 3 Expand and simplify

)23(3)2(2 baba

Ex. 4 Common factor each expression completely.

a) 16124 2 xx

b) 542 963 xxx

Pg. 74 # 1 - 10

MCF 3M Lesson 2.1 Working with Quadratic Expressions

Ex. 1 Expand and simplify:

a) )7()42(3)3(2 xxx b) )3)(7( xx

c) 2572 yy d) yxyx 66

e) 232 x f) 221243 xx

Ex. 2 Evelyn is sewing a quilt as shown below. If the width of the border is x, determine a simplified expression

for the area of the quilt.

Pg. 85 # 2, 3, 5 – 7, 10, 11, 13, 14

MCF 3M Lesson 2.2 Common Factoring

Common factoring is the opposite of the

distributive property.

Ex. 1 Factor each of the following completely.

a) xx 3024 2 b) 243 352842 ppp

c) )1(4)1(3 xxx d) 233234 83612 yxyxyx

Ex. 2 A triangle has an area of xx 4812 2 and a height of 3x. What is the length of its base?

Ex. 3 Show that x3 is a common factor of )3(5)3(2 xxx .

Pg. 93 # 2, 3, 5 – 8, 10, 12. 15

MCF 3M Lesson 2.3 Factoring Quadratics in the form x2 + bx + c

ie: Find 2 integers that multiply to c and add to b.

Ex. Factor each of the following, completely.

a) 1272 xx b) 1892 xx

c) 22 103 yxyx d) 3242 xx

e) 12633 2 aa f) 48164 2 mm

Pg. 99 #2, 3, 5 – 9, 12 - 14

MCF 3M Lesson 2.4 Mid-Chapter Review

Pg. 103 # 1, 3 – 5, 7, 9 - 11

?

MCF 3M Lesson 2.5 Factoring Quadratics in the form ax2 + bx + c, a ≠ 1

When trying to factor a quadratic in the form ax2 + bx + c, a ≠ 1, the first thing you should do is determine if

there is a common factor.

Ex. 1 Factor completely.

2482 2 mm

If there is no common factor, we must factor the trinomial using other methods.

DECOMPOSITION - breaking a number or expression into parts that make it up

- Always check for a common factor

To factor using decomposition, we must find two integers that multiply to a x c, and add to b.

ie: For 3x2 – 11x – 4, Product = (3)(-4) = -12

Sum = -11

Factors = -12, 1

We then decompose the bx term into two terms using the integers found in step .

3x2 – 11x – 4

= 3x2 – 12x + x – 4

We then factor the four terms using a method called grouping. This involves grouping the four terms

into 2 groups of two terms and then common factoring each group

3x2 – 11x – 4

= 3x2 – 12x + x – 4

= [3x2 – 12x] + [x – 4]

= 3x[x – 4] + 1[x – 4] We should now have a common factor that we can factor out.

= (x – 4)( 3x + 1)

If the quadratic expression ax2 + bx + c, a ≠ 1 can be factored, then the factors are in the form

(px + r)( qx + s), where a = pq, c = rs, and b = ps + rq.

INSPECTION (a.k.a. – Guess and Check) Always check for a common factor

For 5x2 – 7x + 2, we want to find two terms that multiply to 5x

2 and 2 integers that multiply to 2.

ie: For 5x2 5x

and x (Never use negative integers for the x

2 term)

For 2 1 and 2 or -1 and -2 , since the middle term is negative, we should use -1 and -2

Try (5x -1)(x – 2) = 5x2

– 10x – x + 2 = 5x2

– 11x + 2 WRONG FACTORS !

Try (5x -2)(x – 1) = 5x2

– 5x – 2x + 2 = 5x2

– 7x + 2 CORRECT !

5x2 – 7x + 2 = (5x -2)(x – 1)

When you check your factors, do it to the side of the page or on a piece of scrap paper.

Ex. Factor completely.

a) 1572 2 xx b) 22 3108 yxyx (INSPECTION)

c) 31710 2 yy d) 22 4133 nmnm

e) 372 2 xx (INSPECTION) f) 3108 2 xx (INSPECTION)

Pg. 109 # 2, 4 – 10, 13

MCF 3M Lesson 2.6 Factoring Quadratics Expressions: Special Cases

Difference of Squares

Expand and simplify each of the following.

a) (x – 3)(x + 3) b) (2x – 1)(2x + 1) c) (3x + 2)(3x – 2)

What do you notice about each of the answers from the above examples?

Ex. 1 Factor each of the following completely.

a) x2 – 25 b) 4x

2 – 81

c) 25x4 – 49y

2 d) 224

25

4

9

1yxw

e) (x - y)2 – 4y

6 f) 256x

8 - 81

g) 22 )2( ba h) 22 )2()1( yx

Perfect Square Trinomials

Expand and simplify each of the following.

a) (x + 3)2 b) (2x – 1)

2 c) (3x – 2)

2

What do you notice about each of the answers from the above examples?

Ex. 1 Factor each of the following completely.

a) 4x2 + 12x + 9 b) 25x

4 – 40x

2 + 16

c) x2 – 12xy + 36y

2 d) 12x2 + 60x + 75

Perfect Square Trinomial can be factored using the methods learned previously, but it is quicker when you

recognize it as a perfect square trinomial. Pg. 115 # 2 - 12