Question

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

Answer 1

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). Here's how it works step by step:

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:
\[
1 \cdot x = 1x \quad \text{(or just } x\text{)}
\]

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

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

Combine like terms (\(-8x + x\)):
\[
2x^2 - 7x - 4
\]

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