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

Factoring Polynomials: Double Grouping Answers

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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
2
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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)
3

Which polynomial is prime?

A
3x3 + 3x2 – 2x – 2
B
3x3 – 2x2 + 3x – 4
C
4x3 + 2x2 + 6x + 3
D
4x3 + 4x2 – 3x – 3
4

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)
5

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)
6

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)
7

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)

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