Question

the polynomial 2x3-5x2+4x-10 is split into two groups 2x^3+4x and -5x2-10 the gcf of each group is then factored out what is the common binomial factor between the two groups after their gcfs have been factored

Answer 1

The common binomial factor between the two groups after their gcf have been factored is
`x^2+2`

Explanation:

Given : The polynomial
`2x^3-5x^2+4x-10` is split into two groups
`2x^3+4x` and
`-5x^2-10` the gcf of each group is then figured out.

To find : what is the common binomial factor between the two groups after their gcf have been factored

Solution : The polynomial
`2x^3-5x^2+4x-10` split into two groups

First group -
`2x^3+4x`

Second group -
`-5x^2-10`

`2x^3-5x^2+4x-10=(2x^3+4x)+(-5x^2-10)`

There is a gcf of 2x in first grouping and -5 in second grouping

`=2x(x^2+2)-5(x^2+2)`

The another common factor between two terms is
`x^2+2`

`=(2x-5)(x^2+2)`

The common binomial factor between the two groups after their gcf have been factored is
`x^2+2`.

Answer 2

2x³ - 5x² + 4x - 10

2x³ + 4x and -5x² - 10

2x(x² + 2) - 5(x² + 2)

(2x - 5)(x² + 2)

The common binomial factor between the two groups after their gcfs have been factored is x² + 2