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

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

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

2. **Outer:** Multiply the outer terms:
\(2x \cdot (-4) = -8x\)

3. **Inner:** Multiply the inner terms:
\(1 \cdot x = 1x\)

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

Now, combine all of these results:

\[
2x^2 - 8x + 1x - 4
\]

Combine the like terms \((-8x + 1x)\):

\[
2x^2 - 7x - 4
\]

So the product of the polynomials is:

\[
2x^2 - 7x - 4
\]

Filling in the blanks:
_ \(2\) _ \(-7\) _ \(-4\)