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 perform the multiplication as follows:

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

Now, we combine all these results:

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

Next, we combine like terms (\(-8x\) and \(1x\)):

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

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

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