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

Answer 1

To find the product of the polynomials \( (2x + 1)(x - 4) \), we will use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms of each polynomial: \[ 2x \cdot x = 2x^2 \]

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

3. Inner: Multiply the inner terms: \[ 1 \cdot x = x \]

4. Last: Multiply the last terms of each polynomial: \[ 1 \cdot (-4) = -4 \]

Now, we combine all these results: \[ 2x^2 - 8x + x - 4 \]

Combine the like terms \( -8x + x \): \[ 2x^2 - 7x - 4 \]

Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ \boxed{2x^2 - 7x - 4} \]