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

Question

x2+
x+

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 (First, Outside, Inside, Last):

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

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

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

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

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

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

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