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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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
2
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Represent the trinomial using 1 positive x2-tile,[___] , and[___] .

A
1 positive unit tile
B
1 negative unit tile
C
12 positive unit tiles
D
12 negative unit tiles
4

Drag tiles onto the board to represent each factor. What is the factorization? x2 + x – 12 =[___]

A
(x + 3)(x + 4)
B
(x + 3)(x – 4)
C
(x – 3)(x – 4)
D
(x – 3)(x + 4)
5

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
7

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)
8

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.
10

The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.

Answer:

Since the trinomial is $x^2 + bx - c$ and its factors are $(x + m)(x - n)$, we know that $m + (-n) = b$ and $m(-n) = -c$. Because $b$ is positive, the sum of $m$ and $-n$ must be positive. This means the positive value, $m$, must have a greater absolute value than the negative value, $n$. Therefore, $m$ must be greater than $n$.

11

Represent the trinomial using 1 positive x2-tile,[___] , and[___] .

A
1 positive x-tile
B
1 negative x-tile
C
12 positive x-tiles
D
12 negative x-tiles
12

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14

What did you include in your response? Check all that apply.

A
The value of m must be greater than the value of n.
B
The coefficient of the middle term, b, is the sum of m and –n.
C
The factor with the greater absolute value has the sign of the middle term.
D
Since b is positive, m must have the larger absolute value.
15

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16

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