To determine which of the options is a factor of the polynomial 2x² + 3x + 5, we need to look at the polynomial and consider the process of factoring. Since we’re not provided with the specific answer choices, we can go through the general approach to finding factors.
First, we check if the polynomial can be expressed in a factored form. One method is to look for possible rational roots using the Rational Root Theorem, but first, it’s essential to analyze the discriminant of the quadratic equation formed:
For a quadratic of the form ax² + bx + c, the discriminant D is defined as:
D = b² – 4ac
Plugging in our values:
D = (3)² – 4(2)(5) = 9 – 40 = -31
Since the discriminant is negative, it indicates that the polynomial has no real factors. Therefore, this polynomial does not factor neatly into linear components with real coefficients, and thus cannot have any real factorization among common integers.
If we were provided specific options, we could evaluate each to see if it divides the polynomial evenly or is a factor through synthetic or long division. However, with the polynomial presented, it remains unfactorable in real terms.