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?

a)2x + 5
b)2x − 5
c)x2 − 2
d)x2 + 2

Answer 1

The common binomial factor between the two groups after their GCFs have been factored out is (x² + 2).

Step-by-step explanation:

To find the common binomial factor between the two groups after their GCFs have been factored out, we need to factor out the GCF of each group. For the first group, 2x³ + 4x, the GCF is 2x. Dividing each term by 2x, we get 2x(x² + 2). For the second group, -5x² - 10, the GCF is -5. Dividing each term by -5, we get -5(x² + 2).

Now, we can see that both groups have a factor of (x² + 2). Therefore, the common binomial factor between the two groups after their GCFs have been factored out is (x² + 2).

Answer 2

2x³ - 5x² + 4x - 10

(2x³ + 4x) + (-5x² - 10)

2x(x² + 2) - 5(x² + 2) = Answer is Choice D. x² + 2