Question

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

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).

We will multiply 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, we perform the multiplication:

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

Now, we combine all these results:

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

Next, we combine like terms:

The \(x\) terms are \(-8x\) and \(x\):

\(-8x + x = -7x\)

So, the final result is:

\[
2x^2 - 7x - 4
\]

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

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