Question

Find the product of the polynomials (2x+1)(x−4) .(2 points) x2+x+

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 are the steps:

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:
\[
1 \cdot x = x
\]

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

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

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

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