Name Date _________ HSA.SSE.A.2 Class

Factoring Special Case QuadraticsKey Takeaways:

Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

Previously, we learned how to factor trinomials of the form x2+bx+c. Today, we learned how to identify and factor two special case quadratics: difference of two perfect squares and perfect square trinomials

Vocabulary: Sum, difference, product, Perfect square trinomials, difference of two squares, Perfect squares, square roots, Quadratic, Binomial, trinomial, Combining like terms, Factors, factorable, Factor ‘completely’ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Everybody Writes!________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Part 1: Activation of Prior Knowledge

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1. Find a, b, and c for the quadratic x2−9, and then factor it. Use an area model to help you.

a=¿

b=¿

c=¿

Factors:

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Part 2: Explore Part 1

1. What are the factors of x2−16?

2. What are the factors of 4 x2−16?

3. What makes these quadratics different than the quadratics we factored yesterday? What do the quadratics in #1 and #2 have in common?

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4. Which of the quadratics below would follow the same pattern? Why?

(a)36 x2−16

(b)9 x2−25

(c)4 x2+16

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Part 3: Explore Part 2

1. What is ( x+7 )2?

2. What is ( x−7 )2 as a simplified trinomial?

3. What is the relationship between each trinomial’s b and c term?

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4. Which of the following quadratics would follow the same pattern? Why?(a)

x2+10x+24(b)

x2−10 x+25(c)

x2+5x+25

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Part 4: Independent Practice (MILD)

1. Which of the following quadratics can be factored using the difference of squares?(1) 2 x2−100(2) x2−81(3) x2+81(4) 4 x2+9

2. Which of the following is a perfect square trinomial?(1) x2+6 x+36(2) x2+8 x+64(3) x2−10 x−25(4) x2−8 x+16

3. What is x2−121 in factored form?(a) ( x−11 )2

(b) ( x−11 ) ( x+11)(c) ( x−121 ) ( x+1 )(d) ( x+11)2

4. What is 9 x4−16x2 in factored form?(a) (3 x−4 ) (3x+4 )(b) (3 x2−4 ) (3 x2+4 )(c) (3 x2−4 ) (3 x2+4 x )(d) (3 x2−4 x ) (3 x2+4 x )

5. What is x2−8 x+16in factored form?(a) ( x+4 )2

(b) ( x−4 ) ( x+4 )(c) ( x−4 )2

(d) ( x−8 ) ( x−2 )

6. What is ( x+7 )2?(a) x2+49(b) x2−14 x+49(c)x2+49 x+49(d) x2+14 x+49

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7. Factor the following polynomials:

A) k2 – 100

B) 36x2 – 49y2

C) 81 – r2

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Part 5: Independent Practice (MEDIUM)

1. Which shows the correct factored form?

2. Factor 16 x4−81.

3. What is a common factor of x2−16and x2+ x−12? a. x – 4 b. x – 3c. x+3d. x+4

4. One of the factors of 16 x2– 9 is…a. 8 x – 3b. 8 x+3c. x+3d. 4 x –3

5. Expressed in factored form, the binomial 16a2 –81b2 is equivalent to…a. (4a – 9b)(4 a– 9b)b. (4a – 9b)(a+9b) c. (4a – 9b)(4 a+9b) d. (4a – 9b)(4 a+b)

Part 6: Independent Practice (SPICY)7

1. Justice uses the equation y=12 x+7 to calculate the cost of his babysitting. Aurel charges at a constant rate, and charges $18 for one hour and $57 for four hours. Which of the following statements is true?

(a) Justice’s hourly rate is $1 more expensive(b) Aurel’s hourly rate is $6 more expensive(c) Aurel’s initial fee is $2 cheaper(d) The two charge the same hourly rate

2. The table below shows the total amount a company charges a homeowner to clean the carpets in different numbers of rooms.

Which of the following equations represents the data in the table?(a) D= 129r+10

(b) D=3 r+7(c) D=29r(d) D=29r+10

3. Which of the following lines contains the point (-1, 4)?

(a) y=4 x(b) y=4 x+8(c) y=3 x−1(d) y=x−5

4. Which of the following shows the equation of the line that is parallel to the line that passes through the points (4, 3) and (-2, 1)?

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(a) y=13 x+123

(b) y=13 x+5(c) y=3 x−9(d) y=3 x+7

Spicy: Open Ended Response

1. AT&T charges a flat monthly fee of $50 plus $0.75 per gb of storage uses. Verizon charges a rate of $35 plus $0.90 per gb used. After how many gb of storage would the two companies price be equal?

Answer: ________________GB

2. If you were planning on using 80 GB a month, which would you use? Why? Explain in the space below.

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Mathletes1.

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“”I’m a mathlete

2. The height of a ball tossed in the air is represented by the equation y=−x2+12 x+3, where y is the height in meters and x is the time in seconds. What is the maximum height reached by the ball? (Solve this problem algebraically, which means without using a graph! )

Genius Round: Find the solution to this system of equations

{f ( x )=x2+2xf ( x )=4 x−2

Name Date _________ HSA.SSE.A.2 Class

Factoring Special Case QuadraticsExit Ticket

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Directions: Complete each problem by showing ALL work. Don’t forget to use MOLE!

1. What are the factors of the quadratic below?

x2−12 x+36

(1) ( x−6 ) ( x+6 )(2) ( x+6 )2

(3) ( x−6 )2

(4) ( x+9 ) ( x−4 )

2. What are the factors of the quadratic below?

16 x4−64

3. The factored form of a quadratic is (2 x−3 )2. Express the factored quadratic as a simplified trinomial.

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Name Date _________ HSA.SSE.A.2 Class

Factoring Special Case QuadraticsHomework

Directions: Solve each problem. Show all work using MOLE.

1. What are the factors of 9 x2−25?

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(a) (3 x – 5)(3x−5)(b) (3 x+5)(3x+5)(c) (9 x – 5)(x+5)(d) (3 x+5)(3x –5)

2. What is a common factor of x2+7x−18 and x2−81?

(a) (x – 9)(b) (x + 9)(c) (x + 2)(d) (x – 2)

3. Factor the expression below.

9 x4−36

Answer:_____________________________

4. Which of the following is equivalent to the expression below:

(4+5 x )2

(a)25 x2+16(b)−25 x2+16

5. What is the solution set to the system of equations seen on the graph?

(a)(-5, -4)(b)(-4, -5)(c) (4, -5)(d)(-4, 5)

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(c) 25 x2+40 x+16

(d)25 x2−40 x+166. What are the factors of the quadratic

x2−8 x+15?

(a) (x+3)(x+5)(b) (x+3)(x−5)(c) (x−3)(x+5)(d) (x−3)(x−5)

7. According to the graph below, f (x)=2. What is the value of x?

(a) -2(b) -1(c) 0(d) 2

8. What is the y-intercept of the graph below? Describe its meaning.

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