AnswersAlgebra IUnit Test

Factoring Polynomials: Double Grouping Answers

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Which polynomial is prime?

A
3x3 + 3x2 – 2x – 2
B
3x3 – 2x2 + 3x – 4
C
4x3 + 2x2 + 6x + 3
D
4x3 + 4x2 – 3x – 3
2
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Factor x3 – 4x2 + 7x – 28 by grouping. What is the resulting expression?

A
(x2 – 4)(x + 7)
B
(x2 + 4)(x – 7)
C
(x2 – 7)(x + 4)
D
(x2 + 7)(x – 4)
3

Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?

A
(2x2 – 3)(4x + 1)
B
(–2x2 – 3)(–4x + 1)
C
(2x2 – 3)(–4x + 1)
D
(–2x2 – 3)(4x + 1)
4

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?

A
(x2)(x + 1)
B
(x2 + 1)(x)
C
(x2 + 1)(x + 1)
D
(x3 + 1)(x + 1)
5

The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping. 10x3 + 35x2 − 4x − 145x2(____) − 2(____)What is the common factor that is missing from both sets of parentheses?

A
−2x − 7
B
2x + 7
C
−2x2 + 7
D
2x2 + 7
6

Which polynomial is prime?

A
7x2 – 35x + 2x – 10
B
9x3 + 11x2 + 3x – 33
C
10x3 – 15x2 + 8x – 12
D
12x4 + 42x2 + 4x2 + 14
7

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?

A
x(x2 + 4) + 5(x2 + 4)
B
x2(x + 4) + 5(x + 4)
C
x2(x + 5) + 4(x + 5)
D
x(x2 + 5) + 4x(x2 + 5)
8

Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?

A
x(x2 – 5) + 6(x2 – 5)
B
x(x2 + 5) – 6(x2 + 5)
C
x2(x – 5) + 6(x – 5)
D
x2(x + 5) – 6(x + 5)
9

Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.Step 1: (6x4 – 8x2) + (3x2 + 4)Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)

A
Faelyn should realize that her work shows that the polynomial is prime.
B
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
C
In Step 2, Faelyn should factor only 2x out of the first expression.
D
Faelyn should factor out a negative from one of the groups so the binomials will be the same.
10

Which shows one way to determine the factors of x3 + 11x2 – 3x – 33 by grouping?

A
x2(x + 11) + 3(x – 11)
B
x2(x – 11) – 3(x – 11)
C
x2(x + 11) + 3(x + 11)
D
x2(x + 11) – 3(x + 11)

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