Factoring Polynomials: Double Grouping Assignment

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.

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Which polynomials are prime? Check all that apply. 15x2 + 10x - 9x + 7 20x2 - 12x + 30x - 18 6x3 + 14x2 - 12x - 28 8x3 + 20x2 + 3x + 12 11x4 + 4x2 - 6x2 - 16

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

Factor 20x2 + 25x - 12x - 15 by grouping. 1. Group terms with common factors. 2. Factor the GCF from each group. 3. Write the polynomial as a product of binomials. (20x2 - 12x) + (25x- 15) 4x(5x - 3) + 5(5x - 3) (5x - 3)(_____x + _____)

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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 ____. The GCF of the group (6x - 3) is ____. The common binomial factor is ____. The factored expression is ____.

7x 3 2x - 1 (7x + 3)(2x - 1)

Factor the polynomial 4x4 - 20x2 - 3x2 + 15 by grouping. What is the resulting expression? (4x2 + 3)(x2 - 5) (4x2 - 3)(x2 - 5) (4x2 - 5)(x2 + 3) (4x2 + 5)(x2 - 3)

B.) (4x2 - 3)(x2 - 5)

Which polynomial has (3x + 2) as a binomial factor? 6x3 + 3x2 + 4x + 2 12x2 + 15x + 8x + 10 18x3 - 12x2 + 9x - 6 21x4 + 7x3 + 6x + 2

B.) 12x2 + 15x + 8x + 10

Lucas and Erick are factoring the polynomial12x3 - 6x2 + 8x - 4. Lucas groups the polynomial (12x3 + 8x) + (-6x2 - 4) to factor. Erick groups the polynomial (12x3 - 6x2) + (8x - 4) to factor. Who correctly grouped the terms to factor? Explain.

Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property, this common binomial term can be factored out. Each grouping results in the same two binomial factors.

Factor the polynomial 3x4 - 2x2 + 15x2 - 10 by grouping. Which product is the factored form of the polynomial? (-x2 - 5)(3x2 + 2) (x2 - 2)(3x2 + 5) (x2 + 5)(3x2 - 2) (3x2 - 5)(x2 + 2)

C.) (x2 + 5)(3x2 - 2)

Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 - 3x - 20x + 4. Her work is shown below. (15x2 - 3x) + (-20x + 4) 3x(5x - 1) + 4(-5x + 1) Talia noticed that she does not have a common factor. What should she do? Talia needs to leave the polynomial as is because it is prime and cannot be factored. Talia needs to group the terms differently. Talia needs to factor out a negative from one of the groups so the binomials will be the same. Talia needs to apply the distributive property to get the expression (3x + 4)(5x - 1).

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