Factoring Polynomials: Double Grouping

Question 1

Use the drop-down menus to complete the statements about factoring 14x2 + 6x – 7x – 3 by grouping.

Revolt · Accepted Answer

The GCF of the group (14x2 – 7x) is .: 7x; The GCF of the group (6x – 3) is .: 3; The common binomial factor is .: 2x – 1; The factored expression is .: (7x + 3)(2x – 1)

Question 2

Use the drop-down menus to complete the statements about factoring 14x2 + 6x – 7x – 3 by grouping.

Revolt · Accepted Answer

D: ✔ 7x

Question 3

Factor the polynomial 3x4 – 2x2 + 15x2 – 10 by grouping.Which product is the factored form of the polynomial?

Revolt · Accepted Answer

C: (x2 + 5)(3x2 – 2)

Question 4

Which statements are true about the polynomial 4x3 – 6x2 + 8x – 12? Check all that apply.The terms 4x3 and 8x have a common factor.The terms 4x3 and – 6x2 have a common factor.The polynomial is prime.The factored polynomial is (2x2 – 3)(2x + 4).The polynomial can be grouped in different ways to factor by grouping.

Revolt · Accepted Answer

A: The terms 4x3 and 8x have a common factor.; B: The terms 4x3 and – 6x2 have a common factor.; E: The polynomial can be grouped in different ways to factor by grouping.

Question 5

Which polynomial has (3x + 2) as a binomial factor?

Revolt · Accepted Answer

B: 12x2 + 15x + 8x + 10

Question 6

Which polynomials are prime? Check all that apply.15x2 + 10x – 9x + 720x2 – 12x + 30x – 186x3 + 14x2 – 12x – 28 8x3 + 20x2 + 3x + 1211x4 + 4x2 – 6x2 – 16

Revolt · Accepted Answer

A: 15x2 + 10x – 9x + 7; D: 8x3 + 20x2 + 3x + 12; E: 11x4 + 4x2 – 6x2 – 16

Question 7

Talia noticed that she does not have a common factor. What should she do?

Revolt · Accepted Answer

C: Talia needs to factor out a negative from one of the groups so the binomials will be the same.

Question 8

Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. What is the resulting expression?

Revolt · Accepted Answer

B: (4x2 – 3)(x2 – 5)

Question 9

(2x + 1)(x – 1)(2x + 3)(7x – 1)✔ (7x + 3)(2x – 1)(7x – 1)(x – 2)

Revolt · Accepted Answer

C: ✔ (7x + 3)(2x – 1)

Question 10

Factor 20x2 + 25x – 12x – 15 by grouping.

Revolt · Accepted Answer

: 78707; : 5

Factoring Polynomials: Double Grouping Answers

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