Question

the polynomial $2x^3 - 5x^2 + 4x - 10$ is split into two groups, $2x^3 + 4x$ and $-5x^2 - 10$. 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? \
\bigcirc $2x + 5$ \
\bigcirc $2x - 5$ \
\bigcirc $x^2 - 2$ \
\bigcirc $x^2 + 2$

Explanation:

Step1: Factor the first group

The first group is \(2x^{3}+4x\). The GCF of \(2x^{3}\) and \(4x\) is \(2x\). Factoring out \(2x\), we get:
\(2x(x^{2} + 2)\)

Step2: Factor the second group

The second group is \(-5x^{2}-10\). The GCF of \(-5x^{2}\) and \(-10\) is \(-5\). Factoring out \(-5\), we get:
\(-5(x^{2}+ 2)\)

Step3: Identify the common binomial factor

After factoring out the GCFs from both groups, the first group is \(2x(x^{2}+2)\) and the second group is \(-5(x^{2}+2)\). The common binomial factor is \(x^{2}+2\).

Answer:

D. \(x^{2}+2\)