Question

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

Answer 1

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

1. **Multiply the first terms:**
\[
2x \cdot x = 2x^2
\]

2. **Multiply the outer terms:**
\[
2x \cdot -4 = -8x
\]

3. **Multiply the inner terms:**
\[
1 \cdot x = 1x = x
\]

4. **Multiply the last terms:**
\[
1 \cdot -4 = -4
\]

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

Next, combine like terms:
\[
2x^2 - 7x - 4
\]

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