Find the product of 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. Multiply the first terms: \[ 2x \cdot x = 2x^2 \]

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

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

4. Multiply the last terms: \[ 1 \cdot -4 = -4 \]

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

Next, combine like terms: \[ 2x^2 - 7x - 4 \]

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