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 \(x^2+2\).
