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

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

Answer 2

Answer:

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

Step-by-step 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 $x^2+2$.