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

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

Revolt · Accepted Answer

(5x2 + 2)(3x – 1)

Question 3

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 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

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 6

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

Revolt · Accepted Answer

x2(x + 5) – 6(x + 5)

Question 7

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

Revolt · Accepted Answer

(x2 + 1)(x + 1)

Question 8

Which polynomial is prime?

Revolt · Accepted Answer

3x3 – 2x2 + 3x – 4

Question 9

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

Revolt · Accepted Answer

(6x2 – 5)(x2 + 2)

Question 10

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

Revolt · Accepted Answer

x2(x + 11) – 3(x + 11)

Factoring Polynomials: Double Grouping Answers

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