To determine which of the given binomials is a factor of the trinomial [tex]\(8 x^2 + 10 x - 3\)[/tex], we will first factor the trinomial completely and then compare the result with the provided options.
The trinomial we have is:
[tex]\[
8 x^2 + 10 x - 3
\][/tex]
After factoring this expression, we get:
[tex]\[
(2x + 3)(4x - 1)
\][/tex]
Now let's write down the given binomials:
A. [tex]\(4x + 3\)[/tex]
B. [tex]\(4x - 3\)[/tex]
C. [tex]\(2x + 3\)[/tex]
D. [tex]\(2x - 3\)[/tex]
We compare each of the factors of the trinomial [tex]\((2x + 3)\)[/tex] and [tex]\((4x - 1)\)[/tex] with the given options.
1. [tex]\(2x + 3\)[/tex] matches option C.
2. [tex]\(4x - 1\)[/tex] does not match any of the options provided.
Therefore, the binomial that is a factor of the trinomial [tex]\(8 x^2 + 10 x - 3\)[/tex] is:
[tex]\[
\boxed{2x + 3 \text{ (Option C)}}
\][/tex]
