AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVFactoring Polynomials: Double Grouping

Factoring Polynomials: Double Grouping Answers

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Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

A
x2(x – 9) – 5(x – 9)
B
x2(x + 9) – 5(x + 9)
C
x(x2 + 5) – 9(x2 + 5)
D
x(x2 – 5) – 9(x2 – 5)
2
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Factor 15x3 – 5x2 + 6x – 2 by grouping. What is the resulting expression?

A
(5x2 + 2)(3x – 1)
B
(5x2 – 2)(3x + 1)
C
(15x2 + 2)(x – 1)
D
(15x2 – 2)(x + 1)
3

Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?

A
x(x2 – 12) + 2(x2 – 12)
B
x(x2 – 12) – 2(x2 – 12)
C
x2(x – 12) + 2(x – 12)
D
x2(x – 12) – 2(x – 12)
4

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)
5

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.
6

Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

A
2x2(6x – 1) + 3(6x – 1)
B
2x2(6x – 1) – 3(6x – 1)
C
6x(2x2 – 3) – 1(2x2 – 3)
D
6x(2x2 + 3) + 1(2x2 + 3)
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

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
9

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)
10

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)

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