Algebra 1: Factoring Polynomials, Double Grouping

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

(2x2 - 3)(-4x + 1) ?????

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

x(x2 + 5) - 9(x2 + 5)

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

x2(x + 11) - 3(x + 11)

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 noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?

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

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

(x2 + 5)(3x2 - 2)

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

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

Which polynomial is prime?

9x3 + 11x2 + 3x - 33

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

x2(x + 5) - 6(x + 5)

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

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).

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

(20x2 - 12x) + (25x- 15) 4x(5x - 3) + 5(5x - 3) (5x - 3)(4x+5)

Which polynomials are prime? Check all that apply.

15x2 + 10x - 9x + 7 8x3 + 20x2 + 3x + 12 11x4 + 4x2 - 6x2 - 16

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

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

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

(4x2 - 3)(x2 - 5)

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

(5x2 + 2)(3x - 1)

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

(6x2 - 5)(x2 + 2)

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

12x2 + 15x + 8x + 10

Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 - 3x - 20x + 4. Her work is shown below. 1. (15x2 - 3x) + (-20x + 4) 2. 3x(5x - 1) + 4(-5x + 1) Talia noticed that she does not have a common factor. What should she do?

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

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 can be grouped in different ways to factor by grouping.