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

Question

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:

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