AnswersCommon Core Algebra I B-ICFactoring Trinomials: a = 1 (Continued)

Factoring Trinomials: a = 1 (Continued) Answers

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1
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Complete the statements to explain how to factor x2 + x – 12 using algebra tiles.

Answers:
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–28
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–3
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–7 and 4
Use double grouping to factor the four terms.x2 – 3x – 28 =:(x – 7)(x + 4)
2
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–28✔ –31

A
–28
B
✔ –3
C
1
3

–14 and 2✔ –7 and 4–4 and 7

A
–14 and 2
B
✔ –7 and 4
C
–4 and 7
4

(x – 14)(x + 2)✔ (x – 7)(x + 4)(x + 7)(x – 4)

A
(x – 14)(x + 2)
B
✔ (x – 7)(x + 4)
C
(x + 7)(x – 4)
83433

Complete the statements to explain how to factor x2 + x – 12 using algebra tiles.

Answers:
Represent the trinomial using 1 positive x2-tile, , and .:1 positive x-tile
Represent the trinomial using 1 positive x2-tile, , and .:12 negative unit tiles
Form a rectangle with the tiles, adding zero pairs as needed. How many zero pairs are needed?:three
Drag tiles onto the board to represent each factor. What is the factorization? x2 + x – 12 =:(x – 3)(x + 4)
83434

1 positive unit tile1 negative unit tile12 positive unit tiles✔ 12 negative unit tiles

A
1 positive unit tile
B
1 negative unit tile
C
12 positive unit tiles
D
✔ 12 negative unit tiles
83435

noneone✔ three

A
none
B
one
C
✔ three
83436

(x + 3)(x + 4)(x + 3)(x – 4)(x – 3)(x – 4)✔ (x – 3)(x + 4)

A
(x + 3)(x + 4)
B
(x + 3)(x – 4)
C
(x – 3)(x – 4)
D
✔ (x – 3)(x + 4)
83437

Which model shows the correct factorization of x2 – x – 2?

A
[Image: An algebra tile configuration. 3 tiles are in the ...]
Option A
B
[Image: An algebra tile configuration. 3 tiles are in the ...]
Option B
C
[Image: An algebra tile configuration. 3 tiles are in the ...]
Option C
D
[Image: An algebra tile configuration. 3 tiles are in the ...]
Option D
83438

What are the factors of x2 – 4x – 5? Check all that apply.x – 5x – 2x – 1x + 1x + 2x + 5

A
x – 5
B
x – 2
C
x – 1
D
x + 1
E
x + 2
F
x + 5
83439

What side lengths should be used to model a rectangle with an area of x2 + 3x – 10 square units?

A
x – 5 and x + 2
B
x – 2 and x + 5
C
x and x + 3
D
x + 3 and x – 10
83440

✔ –28–31

Answers:
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–28
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–3
Identify the values that should be written to complete the X diagram.On the top: On the bottom: On the sides::–7 and 4
Use double grouping to factor the four terms.x2 – 3x – 28 =:(x – 7)(x + 4)
83441

What is the four-term polynomial and factored form of the polynomial?

A
x2 + 7x + 6x – 48 = (x + 7)(x + 6)
B
x2 – 12x + 4x – 48 = (x – 12)(x + 4)
C
x2 + 16x – 3x – 48 = (x + 16)(x – 3)
D
x2 – 16x + 3x – 48 = (x – 16)(x + 3)
83442

Which statement is true of x2 + 8x – 6?

A
(x – 2) is a factor of the polynomial.
B
(x + 2) is a factor of the polynomial.
C
(x – 4) is a factor of the polynomial.
D
The polynomial is prime.
83443

Complete the equation to show two equivalent expressions.

Answers:
Blank 1:3
Blank 2:80208

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