Question

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

Box x ^ 2 + Box x+ Box

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).

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

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

3. Multiply the inner terms:
\( 1 \cdot x = 1x \) (or just \( x \))

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

Now, combine all these results together:

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

Combine like terms:

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

So, the product of the polynomials \( (2x + 1)(x - 4) \) is:

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

In the boxed format, we have:

\[
\Box 2, \Box -7, \Box -4
\]

Thus, your final answer is:

\[
\text{Box } 2 \quad \text{Box } -7 \quad \text{Box } -4
\]