To find the polynomial resulting from multiplying \( (2x + 1)(x - 4) \), we can use the distributive property (also known as the FOIL method for binomials).
-
Multiply the first terms:
\( 2x \cdot x = 2x^2 \) -
Multiply the outer terms:
\( 2x \cdot (-4) = -8x \) -
Multiply the inner terms:
\( 1 \cdot x = 1x \) (or just \( x \)) -
Multiply the last terms:
\( 1 \cdot (-4) = -4 \)
Now we combine all these results together:
\[
2x^2 - 8x + x - 4
\]
Next, we combine like terms: \[ 2x^2 - 7x - 4 \]
Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ \boxed{2x^2 - 7x - 4} \]