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?

−2x − 7

2x + 7

−2x2 + 7

2x2 + 7

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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)

Which polynomial is prime?

x3 + 3x2 – 2x – 6

x3 – 2x2 + 3x – 6

4x4 + 4x3 – 2x – 2

2x4 + x3 – x + 2

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 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 + 5x2 – 6x – 30 by grouping?

x(x2 – 5) + 6(x2 – 5)

x(x2 + 5) – 6(x2 + 5)

x2(x – 5) + 6(x – 5)

x2(x + 5) – 6(x + 5)

Which polynomial is prime?

3x3 + 3x2 – 2x – 2

3x3 – 2x2 + 3x – 4

4x3 + 2x2 + 6x + 3

4x3 + 4x2 – 3x – 3

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

(x2)(x + 1)

(x2 + 1)(x)

(x2 + 1)(x + 1)

(x3 + 1)(x + 1)

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

2x2(6x – 1) + 3(6x – 1)

2x2(6x – 1) – 3(6x – 1)

6x(2x2 – 3) – 1(2x2 – 3)

6x(2x2 + 3) + 1(2x2 + 3)

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

(5x2 + 2)(3x – 1)

(5x2 – 2)(3x + 1)

(15x2 + 2)(x – 1)

(15x2 – 2)(x + 1)

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Factoring Polynomials: Double Grouping Answers

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