Question

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

Answer 1

Sorry, that’s only partially correct Remember that this polynomial expression will generate two x terms. Remember that a positive value times a negative value will equal a negative value.

Answer 2

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) to multiply each term in the first polynomial by each term in the second polynomial.

1. **First**, multiply the first terms: \( 2x \cdot x = 2x^2 \).
2. **Outer**, multiply the outer terms: \( 2x \cdot (-4) = -8x \).
3. **Inner**, multiply the inner terms: \( 1 \cdot x = 1x \) or just \( x \).
4. **Last**, multiply the last terms: \( 1 \cdot (-4) = -4 \).

Now, combine these results:

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

Next, combine the like terms:

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

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

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

Answer 3

Let's carefully expand the product of the polynomials \( (2x + 1)(x - 4) \) again.

Using the distributive property, we'll multiply each term in the first polynomial by each term in the second polynomial step by step:

1. **First**, multiply the first terms:
\[
2x \cdot x = 2x^2
\]

2. **Outer**, multiply the outer terms:
\[
2x \cdot (-4) = -8x
\]

3. **Inner**, multiply the inner terms:
\[
1 \cdot x = x
\]

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

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

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

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

This final result is indeed correct. There's only one \(x\) term combined with \( -8x\) to give \(-7x\). I appreciate your patience, and if there's any further clarification needed, feel free to ask!