Question

Find the product of the polynomials (2x+1) (X-4).
□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's how we do it step-by-step:

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

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

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

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

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

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

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

In terms of the placeholders you provided \( \square x^2 + \square x + \square \), we can fill in the values as follows:
- First coefficient (for \(x^2\)): 2
- Second coefficient (for \(x\)): -7
- Constant term: -4

Final answer:
\[
2x^2 - 7x - 4
\]