To factor the given quadratic expression [tex]\(5x^2 + 7x + 2\)[/tex]:
1. Recognize the expression: We start with the quadratic [tex]\(5x^2 + 7x + 2\)[/tex].
2. Identify the factors: The quadratic factorizes into two binomials. After factoring, we have:
[tex]\[
(x + 1)(5x + 2)
\][/tex]
We need to find which of the given options is a factor of [tex]\(5x^2 + 7x + 2\)[/tex].
3. Compare the options with the actual factors:
- The given factors from the factorization are [tex]\( (x + 1) \)[/tex] and [tex]\( (5x + 2) \)[/tex].
- We compare each option with these factors:
- [tex]\((5x - 2)\)[/tex] is not a factor.
- [tex]\((x + 2)\)[/tex] is not a factor.
- [tex]\((5x + 1)\)[/tex] is not a factor.
Since none of the given options match the factors [tex]\( (x + 1) \)[/tex] and [tex]\( (5x + 2) \)[/tex], the correct answer is:
[tex]\[
\boxed{\text{None of the above}}
\][/tex]
