Final answer:
To determine the value of k, we need to compare the coefficients of x in the expression (2x+1)(x+h) with the original expression 2x²+kx+3. The value of k is equal to the coefficient of x in the expanded form, which is 2h. Without knowing the value of h, we can't determine the exact value of k.
Step-by-step explanation:
To determine the value of k, we will expand the expression (2x+1)(x+h) using the distributive property. This will give us 2x² + 2hx + x + h. We can then compare this to the original expression 2x² + kx + 3.
By comparing the like terms, we can see that the coefficient of x in the expanded form is 2h, and that should be equal to the coefficient of x in the original expression, which is k. Therefore, we can conclude that k = 2h.
Since we don't have the value of h, we can't determine the exact value of k. Therefore, none of the given options (A. -7, B. -5, C. -3, D. -1) can be determined as the value of k.