Question

The polynomial 2x3 − 5x2 + 4x − 10 is split into two groups, 2x3 + 4x and −5x2 − 10. The GCFs of each group is then factored out.
What is the common binomial factor between the two groups after their GCFs have been factored out?


2x + 5

2x − 5

x2 − 2

x2 + 2

Answer 1

$Answer: \\ 2 {x}^{3} - 5 {x}^{2} + 4x - 10 \\ = (2 {x}^{3} + 4x) - (5 {x}^{2} + 10) \\ = 2x( {x}^{2} + 2) - 5( {x}^{2} + 2) \\ = ( {x}^{2} + 2)(2x - 5) \\ Common \: binomial \: factor:2x - 5$

Answer 2

2x³ - 5x² + 4x - 10

(2x³ + 4x) + (-5x² - 10)

2x(x² + 2) - 5(x² + 2) = x² + 2

Answer is Choice D. x² + 2

i hope this helped!