Find the product of the polynomials (2x+1)(x−4) .(2 points)

To find the product of the polynomials \((2x+1)(x-4)\), we can use the distributive property, also known as the FOIL method for binomials (First, Outside, Inside, Last).

1. Multiply the First terms:
\(2x \cdot x = 2x^2\)

2. Multiply the Outside terms:
\(2x \cdot (-4) = -8x\)

3. Multiply the Inside terms:
\(1 \cdot x = x\)

4. Multiply the Last terms:
\(1 \cdot (-4) = -4\)

Now, combine all these results:
\[
2x^2 - 8x + x - 4
\]

Next, combine the like terms \(-8x\) and \(x\):
\[
2x^2 - 7x - 4
\]

So, the product of the polynomials \((2x+1)(x-4)\) is:
\[
\boxed{2x^2 - 7x - 4}
\]