Factoring Polynomials: Double Grouping

Question 1

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?

Revolt · Accepted Answer

2x + 7

Question 2

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

Revolt · Accepted Answer

x2(x + 11) – 3(x + 11)

Question 3

Factor 15x3 – 5x2 + 6x – 2 by grouping. What is the resulting expression?

Revolt · Accepted Answer

(5x2 + 2)(3x – 1)

Question 4

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

Revolt · Accepted Answer

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

Question 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)

Revolt · Accepted Answer

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

Question 6

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

Revolt · Accepted Answer

x2(x – 12) – 2(x – 12)

Question 7

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

Revolt · Accepted Answer

2x2(6x – 1) + 3(6x – 1)

Question 8

Which polynomial is prime?

Revolt · Accepted Answer

2x4 + x3 – x + 2

Question 9

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

Revolt · Accepted Answer

x(x2 + 5) – 9(x2 + 5)

Question 10

Factor x3 – 4x2 + 7x – 28 by grouping. What is the resulting expression?

Revolt · Accepted Answer

(x2 + 7)(x – 4)

Factoring Polynomials: Double Grouping Answers

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