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).

We will multiply each term in the first polynomial by each term in the second polynomial:

1. First: \( 2x \cdot x = 2x^2 \)
2. Outer: \( 2x \cdot (-4) = -8x \)
3. Inner: \( 1 \cdot x = 1x \)
4. Last: \( 1 \cdot (-4) = -4 \)

Now combine all these results:

\[ 2x^2 - 8x + 1x - 4 \]

Combine the like terms (-8x and 1x):

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

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

\[ \boxed{2x^2 - 7x - 4} \]