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).

Let's distribute each term in the first polynomial by each term in the second polynomial:

\[ (2x + 1)(x - 4) = 2x \cdot x + 2x \cdot (-4) + 1 \cdot x + 1 \cdot (-4) \]

Now, let's perform the calculations for each term:

1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot (-4) = -8x\)
3. \(1 \cdot x = x\)
4. \(1 \cdot (-4) = -4\)

Now, combine all these terms:

\[ 2x^2 - 8x + x - 4 \]

Now, combine like terms:

\[ 2x^2 + (-8x + x) - 4 = 2x^2 - 7x - 4 \]

Thus, the product of the polynomials \((2x + 1)(x - 4)\) is:

\[ \boxed{2x^2 - 7x - 4} \]