Answers Summer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVIntroduction to Polynomials

Lesson 7.7: Factoring Polynomials: Double Grouping Answers

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

x(x2 + 4) + 5(x2 + 4)

x2(x + 4) + 5(x + 4)

x2(x + 5) + 4(x + 5)

x(x2 + 5) + 4x(x2 + 5)

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

x2(x – 9) – 5(x – 9)

x2(x + 9) – 5(x + 9)

x(x2 + 5) – 9(x2 + 5)

x(x2 – 5) – 9(x2 – 5)

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

x(x2 – 12) + 2(x2 – 12)

x(x2 – 12) – 2(x2 – 12)

x2(x – 12) + 2(x – 12)

x2(x – 12) – 2(x – 12)

Which polynomial is prime?

3x3 + 3x2 – 2x – 2

3x3 – 2x2 + 3x – 4

4x3 + 2x2 + 6x + 3

4x3 + 4x2 – 3x – 3

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?

−2x − 7

2x + 7

−2x2 + 7

2x2 + 7

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)

Faelyn should realize that her work shows that the polynomial is prime.

Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).

In Step 2, Faelyn should factor only 2x out of the first expression.

Faelyn should factor out a negative from one of the groups so the binomials will be the same.

Which polynomial is prime?

x3 + 3x2 – 2x – 6

x3 – 2x2 + 3x – 6

4x4 + 4x3 – 2x – 2

2x4 + x3 – x + 2

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33

10x3 – 15x2 + 8x – 12

12x4 + 42x2 + 4x2 + 14

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

(2x2 – 3)(4x + 1)

(–2x2 – 3)(–4x + 1)

(2x2 – 3)(–4x + 1)

(–2x2 – 3)(4x + 1)

Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

(6x + 5)(x2 – 2)

(6x – 5)(x2 + 2)

(6x2 + 5)(x2 – 2)

(6x2 – 5)(x2 + 2)

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Lesson 7.7: Factoring Polynomials: Double Grouping Answers

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