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

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 (First, Outside, Inside, Last).

1. Multiply the First terms:
   \(2x \cdot x = 2x^2\)

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

3. Multiply the Inside terms:
   \(1 \cdot x = x\)

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

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

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

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