Question

Select the choices below that can be factored using the group factoring method:

1. 2x₃ - x² - 10x + 50
2. x³ + 10x² + 5x + 50
3. 6x³ - 10x² - 3x + 5
4. 2x³ + x² + 8x + 16

Answer 1

In High School Mathematics, the group factoring method involves grouping terms with common factors and factoring them out. Expressions 2 and 3 from the choices given are the ones that can be successfully factored using this method.

Step-by-step explanation:

The subject of this question is Mathematics, and it pertains to the High School level algebra topic of factoring polynomials using the grouping method. The grouping method involves grouping terms with common factors and then factoring them out.

To identify which choices can be factored using the group factoring method, we'll go through them one by one:

1. 2x³ - x² - 10x + 50: This expression can be rearranged and grouped as (2x³ - 10x) + (-x² + 50), resulting in 2x(x² - 5) - (x² - 50), which cannot be factored further by grouping as the terms do not share a common factor.
2. x³ + 10x² + 5x + 50: Similarly, (x³ + 5x) + (10x² + 50) groups into x(x² + 5) + 10(x² + 5), which can be factored as (x + 10)(x² + 5).
3. 6x³ - 10x² - 3x + 5: Rearranging to (6x³ - 3x) + (-10x² + 5) gives us 3x(2x² - 1) - 5(2x² - 1), which can be factored as (3x - 5)(2x² - 1).
4. 2x³ + x² + 8x + 16: Grouping as (2x³ + 8x) + (x² + 16), we get 2x(x² + 4) + (x² + 16). This cannot be factored by grouping as the terms do not have a common factor.

Therefore, the expressions that can be factored using the group factoring method are choices 2 and 3.